Come on, now. If you don't have an answer for the guy **** off if he already said your suggestion doesn't work for what he wants. He's probably not using it in whatever way you're thinking and/or has already tried any solution that he's saying "thanks but that's not quite what I'm looking for" to.
Por ejemplo. Say he plays a game/uses a program that has a lot of waiting periods, so he wants, during this waiting period, to use a password-protected browser to search the web for whatever he wants. On top of this, he wants to be able to have all the convenience of NOT being in private browsing mode and/or not clearing his history, i.e. bookmarks, restoring the last session, etc. And to top it all off, the app/game he uses? He wants the data saved on the public account.
So there. Multiple accounts does not solve this particular problem. So instead of saying, "Well, I don't see HOW it doesn't solve it" either give the man what he wants or say "sorry I couldn't help." Jesus Christ. Why are people on forums unable to do this?
[Now, to do my part and offer a suggestion]:
I don't know of any password-protected browsers, but you can try putting the browser itself (since Mac is awesome like this) on a thumb drive or possibly a TrueCrypt volume. TrueCrypt, in layman's terms, is a way of creating a virtual, password-protected "thumb drive."