Only the very early ps3s could do that.
Only the 20GB and 60GB PS3 could play PS2 games, but every PS3 plays original PlayStation games.
Actually, the first batch of 80GB models had software emulation for PS2 backwards compatiblity, but it didn’t work as well as the physical PS2 hardware in the 20GB and 60GB models. The later 80GB models (when they dropped the USB ports from 4 down to 2) and beyond dropped that, too.
But yes, all PS3s are backwards compatible with PS1 games.