You're suggesting that there is a new situation for them to enter. Say you have a man born into repressive nation who somehow feels a yearning to be free. But all the information he has at hand tells him that there is no where to be free, what he has is the best there is. He may feel discomfited in his current situation, but he doesn't really know why and he doesn't know where he can go or what he can do about it.
...unless there is a nation of freedom that has a consulate in that repressive nation, and somehow from that consulate there is information of a place where freedom exists, and he can see that freedom through the windows of the consulate, and see through the gates people living in that freedom. And the consulate offers asylum.
That's the purpose of the Body of Christ--to provide that asylum. But if there is no such consulate and no asylum, you can't expect that man to be anything but discomfited.
Hmm.
Okay I may be looking at this from a "spiritual materialist" POV (I just made up that term for the sake of this conversation. I suppose it's more equivalent to "immanence").
The scriptures, for example, are replete with one example after another of individuals having physical encounters of the "supernatural" variety (I'm not a fan of that term in the way most people use it, because I believe when they use it that it they are using it in the sense that an events that takes place in the physical/material reality (i.e. the universe as we know it) is ONLY transcendent, which makes the term near useless imo. Another topic). That is to say, they are consistently seeing things, interacting with things, etc ... that are not just within their minds (according to the accounts) only. Thus, the scriptures for example, though there may be cherry-picked examples of "no one has seen God", etc and so forth ... such examples are rather vague when taken into context of those who DO apparently see Yahweh, Elohim, "God", various types of "angelic" beings, etc. It's not just burning bushes and healed blind men. It's beings that others recognizes as being "other", so on and so forth.
Now regardless of the validity of any of the scriptures or not ... whether we're talking about purely made up fiction, the real deal and we haven't explained it, drug induced hallucinations from gas coming out of caves, borrowed and morphed mythology ... I see these themes continuing on into the NT. People still interacted with and saw "angelic beings", and even the Holy Spirit accounts sometimes involve physical manifestations, etc.
Having said all of that, it's my partial understanding that one of the ramifications of the Jesus narrative (and one of the points of Jesus' purposes in the first place) is the opportunity for human beings to become something "new" ... spiritually speaking. A "son of God", or child of God, etc. This new spiritual nature was the result of one receiving the Holy Spirit, for example ... and one of the reasons a believer may be asked if they had received the Holy Spirit, so on and so forth.
It's my understanding to some degree, that the "Spirit" is a *thing*. That is to say, it isn't just treated as a concept. It was by the Spirit that "miracles" were performed, people became something "new" spiritually, so on and so forth. In other words, it reflected in reality, material/physical reality. It was an "entity". When one received it, they too experienced a change and became something new.
This is contrasted to one who "just believes", as I read it. A believer "believes". But that doesn't necessarily mean they have received this new nature and *change*. Belief involves a perspective on the veracity of a concept or thing in which one is using their mind/brain lol. Nothing necessarily "spiritual" about that. Anyone can have a belief, or lack a belief. Depending on new information or change in input, perhaps one's beliefs will change as well. If you experience brain injury, disease, etc lol ... your beliefs may change radically obviously lol, as your ability to even perceive reality has become impaired. IOW, I'm trying to point out it's basically "just biology". It is the "Spirit" component that is unique in regards to actually changing a person into something "new" and having this reflect in ways that may distinguish them from "people who have beliefs" only in such a context.
I believe perhaps that the average "Christian believer" equates belief and the mind with "Spirit", and is essentially why the average believer has to consistently appeal to arguments, their own mental constructs, pointing to the accounts of others, appealing to emotion/etc in order to try and discern a "change" ... or they attempt to discern who is or isn't a "true believer" by observing changes in moral behavior, which often involves various forms of mental discipline and mental gymnastics, sometimes denial ... because there is nothing "Spiritual" they can point to. The majority of what they are pointing to and using as a reference is within their own mind/feelings/etc, or the claims of someone else. IOW, they are appealing to JUST their own belief and assuming that belief is the same as something "supernatural". Thus, feelings become supernatural, thoughts become supernatural, and changes in behavior become "supernatural". When it's all "in their mind", or I suppose I could say, "in their body" lol. It's a false identification. I think this is one reason why, oddly enough, the claims of the believer often are contradicted by the very scriptures they continually point to. Those scriptures are rife with examples of material/physical events taking place, even on into the NT. Even Paul asked other believers if they had received the Spirit yet for example, etc. Yet the average believer often claims transcendence, I think, in order to align with their own reference point ... their lack of anything to point to apart from their own mental constructs.
So having said all of that ... circling back around to Graham ... entering a "new situation" as it regards
belief, I don't see where that's necessarily the case of what he's saying, where a person is now entering a new system of belief or leaving their old one behind, etc. Because one could arguably have a "spiritual change", which renders their "belief system" irrelevant. Taken with the above understanding in mind ... when Graham is talking about the "light", if one were to equate that with "Spirit" for example ... a potentially material "thing" to some (pseudoscience at this point) ... then Graham is actually talking about a
change within the nature of the person. Not an emotional change, or mental status change, but a "spiritual" change. Thus the beliefs of the mind ... become irrelevant at that point in some capacity. Whether they keep believing "whatever" or not, that "spiritual change" has taken place. That is the new situation, and it didn't involve coming out of a belief system or not.
I'm not saying that is what Graham was definitively saying or not ... I tried not to add to what he said or claim to know what he meant definitively. I'm putting it out there to show that, depending on one's interpretation (hundreds of thousands of them within "Christianity"

) ... one could hear what Graham was saying and presume he was meaning something other than addressing "belief".
ETA: To circle it back around to your own analogy ... that person who is oppressed in that nation, wanting to be part of the "free nation" they see and understand through the consulate ... from the above perspective, once the "change" occurs, they go from being a citizen of an oppressed country, to a citizen of the free nation automatically. Even though their position hasn't changed, their citizenship status has now changed. They may still be discomforted in their environment, but they are now a citizen of another place, regardless of where they are standing.