under FAA rules the student is PIC
My view on this is that an ab initio FAA PPL student is indeed PIC because he is flying on the privileges of his Student Pilot Certificate (normally issued by the FAA doctor on the initial medical).
But a pilot doing a BFR, who is
out of date on his BFR, clearly cannot be PIC. If he could be PIC, there would be no point in needing the BFR.
In the FAA IR, this is taken care of by the student already having a valid PPL and the flight being
actually in VMC.
Incidentally, and I don't have a reference for this but I think the FAA SPC is valid USA only - this would prevent an ab initio FAA PPL in the UK for example unless the student had some other license enabling him to be PIC.