I was wondering myself about how this is addressed. Most of the skill feats from the backgrounds have prerequisites so it seems we are being forced to take training in a particular skill if it calls for it in the prerequisites. Or do we ignore any prerequisites during character creation? In my opinion, background selection should have came after skill training.
Edit: To answer your question though from my perspective if you don't get the trained skill for the background skill feat, you don't get the benefit of it. It's essentially useless without it.