This is unlikely, but I thought I'd ask it anyway, fwiw.
Apparently, Sony made it possible at some point for psp games to be programmed (by the game developers of course) to be played on ps2 (yes, I still have one- and love it), so I'm wondering if they continue to do so or have they dropped this?
Also, does anyone in the game industry even bother to make them at all compatible with this old console anymore?
The only thing I can think of related to this is that a few PSP games were ported to the PS2; OP, are you sure you aren't confused with these games?
This is where I got my info, fwiw:
http://www.theregister.co.uk/2004/03/03/sony_confirms_psp_to_ps2/