Can't you solve the NAT3 anyways? I dunno, it is unrelated to the problem at hand but I wouldn't like it if voice chat was blocked during online gameplay...
NAT2 can only be better.
But yeah, about this issue: can you try anything of the following list:
Deactivate your main PSN account from your system, then reactivate it again.
Deactivate your main PSN account from your system, delete the user account associated with it, delete WipEout HD from your hard disk, back up your save game and delete it from the hard disk. Create a new user account with the same name, log back into your PSN account, download WipEout HD and start with a new save file. If that works, try with your save file. If it doesn't work, it's a glitch and the save file most likely.
Last thing I can think of is a complete format of the PS3 system. Be sure to back up the stuff before trying that.