Yes, but sometimes the facts don't leave it open to interpretation.
If Paul, for example, was writing to answer a certain problem that a church had, or correct a certain heresy or tell them how to act in a particular situation, that is the background of a particular Scripture - and we do not have the right, or authority, to interpret it to mean something else. There are false teachers who have said, "never mind the commentators/orthodox preaching, I have been inspired to interpret this passage in this way."
Interpretation is not the same as application. Even if a Scripture means X, and was written only to certain people, the Holy Spirit can still apply it to our lives in a certain way.