It has to be a provider from the MTF to which you are assigned. Yes it can be a psychologist or psychiatrist, provided they have 'Convening Authority (CA).'
'Out in town' provider is a no-go. (Navy) Manual of the Medical Department (MANMED) 18-9 and 18-24 tells the LIMDU process from top to bottom. Note: not all LIMDU statuses are determined directly by a med eval board (MEB). My provider has CA, so he entered my LIMDU directly in to the system.