wrote
In a similar vein, does an instrument checkride count as a BFR? I
thought it did since it added a rating to the ticket.

It does. However, an instrument instructor ride does not - even
though it is the same ride (only from the right seat).

Of course there's no reason for it - it's just our policy.

BTW - there are a handful of CFII's out there who can't do BFR's
(because they only have the IA rating on the CFI certificate, not ASE
or AME) but they are very much the exception rather than the rule.
Further, I can't for the life of me imagine a situation where I would
be comfortable signing off an ICC and being unwilling to sign off a
BFR. In general, if you're doing an ICC and want a BFR as well, just
ask. Most instructors won't think twice about it.

Michael