That's strange. I've just installed foobar2000 and it indeed plays the files from the beginning. It's certainly not related to a skip time, since the issue happens to a few files, not all of them.
I guess it's some settings that I messed up in MB. So, i'll just reset musicbee. I need an advice before reinstalling it. I'd like not to lose track ratings. Everything else, I can lose it with no problem. What do I do? Thx.