Instructor medical currency

'An airplane instructor may exercise the privileges
of that certificate without a medical. The 'student'
must be qualified to ACT as pilot in command since
the instructor cannot be.'

I cut this from the ASA discussion group, I lurk there
and cannot find a link to register to post. This is
not an attempt to backdoor the poster, just asking
this question:

If a pilot is still current while receiving a BFR,
the instructor is not the pilot in command? And if
the pilot receiving the BFR is still current, then
instructor does not need a current annual?
Curious about this.