Nobody lied to you. How hard can it be? If you can listen to music files form XMB (PSP menu), then you can listen to them in GT.
OK, look, I'll try to explain it as easy as I can, if you still don't get it - you've got a problem...
Let me ask yo a few questions first:
-Is your GTPSP pirated?
No, it was purchased brand new by myself
-Is your PSP hacked?
Same answer as 1st question
-Can you listen to music from the XMB menu?
Yes, i have imported the exact same music folder from my PS3 that i use for my GT5 game music
-Do you have any music files at all on your PSP?
As above
-Does your custom music work with other games?
Only other game i have for the PSP is Resistance: Retribution which doesn't have that option
-Did you pass driving challenge B in GTPSP?