Good exegesis determines what was said, who it was directed at, why it was said. What Jesus said may be for us, for our education in terms of law and grace, but not necessarily to us as direct instruction. What Jesus taught while on earth was to unconverted Jews, because His ministry at that time was not for Gentiles, but for the "lost sheep of Israel".
When Paul said that the departure of the unbelieving spouse (for whatever reason as I have previously stated), the remaining spouse is no longer under bondage, he meant that they can adopt the attitude that they were never married in the first place. The marriage vow has been broken and therefore the remaining spouse is not longer subject to it. Therefore there is no prohibition on remarriage.
Notice that the Scripture says that it is the person who breaks up a marriage and then marries another is the one committing adultery. Again we have to use good exegesis to determine who Paul was teaching, and why he taught it. Basically, he was writing about those who were divorcing their wives on some religious principle and not for the cause of adultery, domestic violence or desertion. Therefore we must adopt the three rules of good exegesis:
1. context
2. context
3. context
For this reason we can't impose a blanket "size fits all" approach to what Paul taught about divorce and remarriage, otherwise we are adding to what Paul taught under the inspiration of the Holy Spirit.
When you said about God confirming something, the only way He confirms anything is that it is clearly written in His word and is understood by good exegesis through the context in which it was spoken.
A couple of additional thoughts:
Paul spoke to three groups of Christians (not to pagans...none of his letters were to pagans):
Unmarried believers,
Believers married to believers,
Believers married to pagans.
Paul is speaking to a new situation, believers married to pagans, for which a specific lesson from Jesus was not available. Jesus never spoke to that context. Hence: "
To the rest [believers married to pagans] I say this (I, not the Lord)...." This doesn't mean it can be ignored, because Paul a few verses later affirms that he is speaking by unction of the Holy Spirit (verse 40).
This line by Paul is often overlooked in this discussion:
For the unbelieving husband has been sanctified through his wife, and the unbelieving wife has been sanctified through her believing husband.
This marriage is recognized by God is because of the belief of the believer. It is not recognized by God separate from the belief of the believer. If the pagan leaves the marriage, he or she also leaves the covering of the believer's belief.
Paul defined his terms (he usually does). He defined what he meant by "bound" a few verses later:
A woman is bound to her husband as long as he lives. But if her husband dies, she is free to marry anyone she wishes, but he must belong to the Lord.
It is clear here that to be "bound" means explicitly, "not free to remarry." Thus, when Paul has said, "The brother or the sister is not bound in such circumstances," he is making a specific rule for a specific situation. If "bound" means "not free to remarry," then "not bound" means "free to remarry."
Essentially, he's saying that when the pagan leaves the sanctifying cover of the believer's belief, the unbeliever is dead.