Basement – Does a bedroom have to have a closet

Water IS getting to it. There IS water there. You cannot fix it by covering the wet. You must fix it by stopping the water from getting to that point.

Check your gutters. Do they tend to get clogged? Are the downspouts set so the water is directed away from that area?

Check the grading in that area.

If all of this checks out, then the water is getting through the wall. There may be a crack. You may need to dig down and apply water proofing in that area, or repair the crack.

I'll answer the second question first:

Where would I go looking for any such information for my location?

Your city's building and code inspector's office.

But note that because something is to code doesn't necessarily mean it has to be done that way--provided you can show why your way is better. Which leads to your first question:

Does anyone know if the concept of vapor barriers ever come in to the code compliance of finished basements?

It does in many places, but today is highly discouraged from most modern building science perspectives.

When I finished my last house's basement, it was in a place that required plastic vapor barriers. I did a lot of research and came to the conclusion that it's a terrible idea and was able to convince my code department of that. Details of that can be found in my answer to the question here:

https://diy.stackexchange.com/a/8644/1209

Note the links provided in the comments by Brad Mace which point to Building Science Corporation's recommendations--which were the same ones I went from.

The executive summary of why vapor barriers are bad in a basement is that a basement will often have moisture problems on EITHER side of the barrier. In both cases, you'd be trapping moisture rather than letting it escape. It's better to allow a certain amount of moisture permeability.