These people are right. The playing has to become pretty much a part of you before you can begin to sing over it.

The other thing that helps me is to find the spots in the guitar parts that line up with the vocal part. Even if they don't necessarily line up completely, you can find a spot where a word may begin slightly after you hit a certain chord.

I do this quite a bit until the feel becomes more natural to me, and it has opened plenty of doors for me. Let me know if that makes sense :)