I had the same problem as BigGarb, but I think I got it covered.
In Leopard, I removed the system fonts as shown in the link that Brad posted. But I couldn't find the protected fonts folder in Snow Leopard, they seemed to have moved it. So I gave up on that.
Someone suggested trying to put the fonts in InDesign's font folder. I didn't even know it had one until today! It seems to have worked. The missing fonts from the Post Script version of Helvetica Neue now show up in InDesign, which is where I do most of my design work.
I didn't check Photoshop and Illustrator until after I placed the fonts in the InDesign font folder, but the fonts seem to working fine there too. I speculate that the conflict never effected those programs in the first place.
It appears, at the moment, that I won't have to remove the system fonts, I can ignore the conflict, and everything will be okay. Woohoo!