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I'm not sure I agree with your hair-splitting. In everything official I've
seen from the FAA the matter seems to revolve only around whether the pilot
is compensated for acting as a pilot (beyond sharing of expenses).

You haven't looked very hard.

As a
private pilot you are certainly allowed to provide transportation to another
person, provided no compensation is paid, regardless of whether you would
have otherwise undertaken the flight.

This is certainly NOT the case. The FAA has repeatedly struck down ride
share operations that involve no money changing hands (not pilot compensation,.
not even expenxes). There are two things the FAA has interpretted that throw
a monkey wrench into things: non-monetary compensation (such as the accrual
of flight time), and carrying passengers in air commerce (not a private vs. commercial
issue but a part 91 vs. 135 one).