The downloadable copies are likely using software emulators specifically tailored for each game (and are packaged within the game files). The PS3 Slims just don't have the generic emulator or the Emotion Engine required to run physical PS2 games.
The Slims dont actually hace any of the PS2 hardware required to play PS2 games.
Its the same with DS and GBA. The DS cant emulate GBA games in DS mode because there isnt enough overhead processing power (not to mention some cheat with onboard processors).
The PS3 cant emulate PS2 games in PS3 mode and there isnt an option for PS2 mode because the hardware isnt there.