In multiple instances in Star Trek: Voyager, this sequence of events happen:
- A character asks the Doctor how he is able to exist outside of the holodeck/sickbay
- The Doctor informs them of the mobile emitter
- The character disables or steals the mobile emitter
This is evidenced in these occasions:
- Equinox; Captain Ransom's EMH (minus ethical subroutines) steals the mobile emitter
- Revulsion; Dejaren, the pshyco hologram that killed his humanoid crew damages the mobile emitter
Among other examples.
From what I see, the Doctor has a couple of options:
- Don't tell anyone about his mobile emitter
- Conceal the mobile emitter (such as tucking the mobile emitter underneath his sleeve)
Why wouldn't the Doctor simply conceal the existance of the mobile emitter?