Mark Hansen wrote:

As PIC, the CFII would be the one officially accepting the clearance (or
not) - non-verbally. The student would only be copying it to paper and
reading it back.

Is this right?

That's it. You could have your two year old ask for the clearance, or
even the guy at the front desk of the FBO, but the PIC on board is
accepting the clearance by launching a flight in accordance with it.
In the case of the student making the radio calls, he or she is just
the conduit.