Medical Director starts with a weapon permit.

[warcrimes]

I think it makes sense, flavor-wise.
The barman and the RD aren't crewmen who've been given weapons as part of their authority- barman's got a shotty under the ledge for stickups, and the RD's got this wackjob needleyshoot he's ostensibly cooked up while bored in the lab. It's not like the other jobs where you've got NT-issued equipment- it's v.much at your own perils, imho.