If they're not actively engaged in a naval exercise or actual warfighting requiring them to maneuver outside the Navigation Rules[0], they are subject to the rules the same as any other vessel - and even then, that's a pretty hard argument to make without actual shots fired in anger. Considerations are made in the rules for special requirements for lighting of naval vessels that, by the nature of their design, are unable to comply with the rules. However, the rules regarding avoiding collision apply to everyone, at all times.

[0] https://www.navcen.uscg.gov/pdf/navRules/CG_NRHB_20151231.pd...

I can't imagine that would be the case in the context of at least this latest collision. On a civilian waterway. They don't appear to have been on maneuvers. And by all accounts one of the most crowded waterways you can sail through.

That does not seem like the context in which you would want to not telegraph maneuvers. Either way it's still a training and culture issue if they can't recognize the difference between the two contexts.

It's worse opsec to needlessly crash into other ships...

The Trump school of opsec: Never reveal your plans to anyone, not even your own allies or subordinates. This way your enemy will be maximally confused. So will your allies, but... oh, look over there!