For the games, sure...
But once you start making a movie, the rules change. It's not a complete copy of Indiana Jones, but their is more than enough to assume that the games are highly reminiscent of the franchise. If what is produced seems to too similar to Indie, which if taking inspiration for the games, it might, then Sony it just going to have to deal with Disney coming after them. And that is not pretty.
Tomb Raider is Indiana Jones and another one of those just came out not too long ago.
I wonder what is causing the directors to bounce. Are they wanting to do their own thing and Sony/Naughty Dog is telling them no? Are they having trouble getting everything they need (Cast, location etc) in a timely fashion and the directors bail for other projects that are actually taking place?