The reason it wouldn't work with the PS2 is very simple, but also technical.
In a traditional, phat ps2, the controller chip that is responsible for the usb/firewire ports is in fact the same CPU (along with 2MB RAM) that ran the PS1. When a PS1 disc is inserted, the bootloader does some funky logic that turns off the EE and uses the GS for handling graphics, since the PS2's GS supercedes everything that the original PS1's graphics chip could do. It then is running off its MIPS chip for the primary. So, by that, ps1 games off usb on a ps2 won't work because the EE is turned off, along with the USB ports, for that compatibility.
I can't exactly explain it for the neutered slim PStwo, since that one migrates everything to the EE, and melds the EE and GS together in the same silicon package... but I can only imagine that (with as lazy $ony is) they would engineer the revised hardware to behave similarly.
The software emulation for PS1 on a PS3 is the same, but is more accurate largely because the PS3 is so much more powerful to be able to handle things better. PS2 off external is not possible unless you maybe have a BC model in the first place... but PS1 should be more likely.