There's 2 models of the Phat, the one that does software emulation (the Phat PS3 with 2 USB ports) and the other with hardware emulation (4 USB ports).
It's true that models with 2 USBs do not have any PS2 hardware and can only use netemu/softemu, but those don't officially play PS2 discs in the first place...
CECH-A and -B have "full" PS2 Slim 75000/90000 integrated CPU/GPU, with metal IHS (which itself has some problematic games, compared to earlier PS2s) - and they weren't officially released in the Australian, British, or Continental European regions (02, 03, 04)
CECH-C and -E (and the unreleased -D and -F) have only the GPU (because it can't be emulated at full speed/accuracy by a PS3 already emulating the CPU), with black plastic chip. CECH-C was the oldest model officially for those 3 regions...
All others don't have any PS2 hardware, never officially played PS2 discs, could only have played PS2 Classics packages without a Cobra cfw (and by coincidence, 2 usb ports were removed at the same time)
The confusion comes due to some calling these 3 types of PS2 mode "hardware, software, none" and some others "full hardware, partial hardware, software" (and neither way is correct when taken literally without further explaination)