This specific thing bugs me a ton. CEX2DEX CFW machines *SHOULD* run them, but sometimes (most if you ask me) have some issue and need to be resigned for CFW anyway. If you have a disc, rip it with PC, transfer it to the PS3 (using my guide), and if there is an error on bootup then resign the eboot.bin accordingly.
I forgot to add (since I only now realized you have that Hitman disc, and that's PS2) A CFW PS3 will absolutely play PS1 and PS2 games assuming you use Cobra PS2 support (sometimes it rejects a game for me unless I use that)
What CFW are you running? Rebug (with Rebug toolbox modifications) is probably the best setup you can shoot for. If you want me to try running an ISO of that hitman build I can (PM's obviously)
I am running lastest REBUG, all the other PS2 games run just fine, that beta of Hitman just won't boot up completely. Both from HDD and disc.