Judah wrote:

If both I and the CFI are club members, who is providing the aircraft - me or
the CFI? (Presumably, I'm paying for it that day.)

This is a dodge that many clubs do. They claim they are renting the
plane and you have to go deal with the instructor (who are not their
employees) separately to avoid the 100 hour inspection.

Frankly, we did the 100hours anyway. There is maintenance that
needs to be done then anyhow and for things like 172's the
inspection when done on a recurrent basis is a no brainer.

Also remember than an annual resets the 100 hour clock. Techncially
since we had a cheap IA doing our maintenance, we did annuals every
100 hour.