Fine, Hulk was a poor choice. We'll go with Thor, who was viewed as a Schizo with God-like power for most of the series. Whether he was officially on the team or not, he was a member in everything but name. That doesn't qualify as a PR nightmare to you?
Not really...Just about every member of the team had issues that were kept on the DL. Hank being abusive, Janet being a mutant, Bruce being Hulk, etc.