PSOne Compatibility?

I realize this is a sad, annoying question. I apologize in advance. But I've been looking everywhere and I can't seem to find the answer.

Is it true that all PS3 models are backwards compatible with PSOne games? I have a 120GB slim, and I was about to buy a couple PSOne Classics from the Playstation Store, but then I thought I remembered reading about how Sony was getting rid of PS2 compatibility but PS1 games would still work. I ask because I have a library of old PS1 games at my parents' house, and I'd rather just dig those out than pay another $5.99 to Sony.

Again, I apologize if this is common knowledge.

http://us.playstation.com/support/answer/index.htm?a_id=1767

I recommend digging those games out, you might find something amazing.

Awesome. Thanks guys.

Now if only the Stimulus Package would come out already.