We were told by who?Examples:
- We're told that nothing can catch up with the Prometheus, but oh wait, here are 4 Starfleet vessels that have caught up and are ready to save the day.

Common type of comedic trope. It's a tv show. It's not a real military ship. After all, Andy Dick was in this episode...So what?...really?- Somehow the Doctors unwittingly initiate a warp core overload on the Prometheus, but neither actor is invested into the moment at all, seemingly expecting the scene to be cut. The warp core overload is halted after pushing a few more buttons. Crisis averted.
I just checked that scene. It's barely noticeable. Would you be able to do it better?- Ensign Kim tests out a potential EMH replacement for the Doctor, and as the replacement Doctor is reciting a section from a medical textbook (from memory), Robert Picardo's eyes are going side-to-side, clearly reading cue cards that are nearby off-camera.

The Prometheus EMH barely described the current events. You are also ignoring the reason he tried to deactivate himself. The regulation he cited simply stated that he is supposed to be inactive during that type of situation. He wasn't going "ohh, that's one of the bad guys! I better go away". He likely is more tied to his programming than the Voyager EMH...- For whatever reason, the Prometheus' EMH has info on Starfleet deployment as well as current political/military knowledge about the Federation-Dominion war. He also refuses to treat the injured Romulan because he's "the enemy."