He is indeed aware of a different box to earth-bound people, but the show has repeatedly represented the Doctor as very prejudiced against the military.
That is also true, but a separate issue. Military works by strict rules, regulations, tactical thinking etc. The Doctor is at heart a rebel and likes to go for crazy solutions - breaking the system, taking it apart, then putting it back together differently.

Whatever happens, the Doctor can just nip back and tell that scientist to have fewer drinks and make sure Erica has a spare pair of glasses.
Unless that creates a paradox. And if he's part of events, that's quite probably not an option...