Yes, while the term "hero" may be hyperbolic, it is noble that Harrison Ford uses his wealth and privilege to help people. Many celebrities use their wealth extravagantly, without any consideration for the ways their power can be productive. It is also humorous, given Harrison Ford's acting career, that he chooses rescue people, even in the real world.
Anytime anyone does anything to help others it makes them a hero. Why would Harrison Ford be disqualified from this just because he uses his personal plane? He should be praised for rescuing people. Not everyone would do that unless they were told to. I don't think the personal plane has anything to do with being a hero.
Harrison Ford using his personal plane to rescue people does make him a hero, because saving even one life is an unforgettable act. The fact that he cared about people who would perhaps have been left stranded or marooned without his help speaks volumes not just about his reel life persona, but about him in real life as well.
Using your private plane to rescue people is definitely an extremely selfless act. However, I am not sure I would consider it heroic without knowing the circumstances surrounding the rescues. To me, people who fight for our freedom daily are true heroes. People who do decent things to help mankind are wonderful too, obviously, and may be considered heroes to those who they have helped. But to call Ford a hero outright may be a bit much,