Is there any way other than watching a movie or trusting IMDB to see the credits (such as closing credits) of any movie?
I would assume that the industry itself must store this kind of data somewhere since this is a practical necessity (e.g. people need to be paid residuals,...). There is for instance the Motion Picture Credits Database:
... and the Official Screen Credits for Academy Awards Consideration (same page, I'm not going to copy-paste the entire description).
This page mentions several databases, some are only available to UCB users.
The only way to find them is to get your copy of the movie or find it for free online. There is no other way for watching closing credits or end credits of any movie unless you have a copy (or trusting IMDb as you said). Most of the movies can be found nowadays for free online, you can just search for them and skim over the credits.
Rare are the people who are interested in closing credits, this is why American producers decided to cut them off music videos.