I agree, but it's pretty tough to force people to care no matter what order in which you try to do it. I tend to think that if you teach them first, it all goes flying over their heads, then you have them watch the dramatization and suddenly they think "oh now it all makes sense" and remember the movie version.
Alternately, I'd think showing the movie and giving them a much more approachable and entertaining introduction to the subject which piques their interest will yield better results as far as further research and retention is concerned.
That's just my experience anyway, personally as well as observationally. To simplify into examples pertaining to...let's just say Saving Private Ryan, since that was mentioned.
If someone learns about WWII, they get a whole lot of information, maybe some context, and probably remember very little about it. Then they watch Saving Private Ryan and place that narrative into whatever framework they have managed to create, and it fills in the details for them (some of which are incorrect, inaccurate, or speculation, etc.) and then that is what they remember.
However, if they watch the movie, they may be intrigued enough by the drama and the history to then go research the actual events surrounding the movie plot, and in so doing discover the inaccuracies, and fill in all the blanks and inaccuracies with the real information....but with the movie as a sort of "memory framework" that they base all the research on.
This is all, like I said, just how it works for me.
The end result is that the better a movie was, the more I tend to know about the actual history of the subject.