After that movie, the influence the DoD had was much more subtle if it was there at all.

Their involvement is blatant. They literally have a near century long intimate relationship with Hollywood as a well established recruitment tactic. It's hardly a secret.

https://en.wikipedia.org/wiki/Military%E2%80%93entertainment_complex

https://www.military.com/undertheradar/2018/03/22/how-why-defense-department-works-hollywood.html