Safety pilot - logging cross-country

Can
the safety pilot be PIC even while the left-seat pilot is not under
the hood? ... seems like a stretch to me.

The seat occupied isn't important; I take it you mean "pilot flying".
Given that, yes, the safety pilot can =be= PIC. It's the =logging= of
PIC time that is the issue. It sounds like he's trying to say "yes" and
not quite succeeding.

Jose
--
You can choose whom to befriend, but you cannot choose whom to love.
for Email, make the obvious change in the address.