Correct, the project specific emails only work if they're a member of the project or team that the project belongs to!
@Advocate, I would advise setting up a catch all email like marketing@yourorg where people send requests there, and you set up the auto forwarding like @Diakoptis recommended - sending them to a catch-all requests project that you or whomever have task creation notifications on for.
The only issue with this method is that there's no back and forth via email the way there would be if you added them to the org, if you needed answers from them you would have to email or slack them etc. I believe there are solutions out there (3rd party), similar to Customer Support functions - where people use Asana for CS purposes. However if you're looking to not add a 3rd party for reasons, then the forwarding would be the way to go IMO! =)