Ah. A crucial difference. You can
receive instruction in your own airplane and pay an instructor without complying with the 100-hour inspection rule because
you're not offering the airplane for compensation or hire to another person. You're paying the instructor for his or her services as an instructor.
Note that
91.409 says:
...and no person may give flight instruction for hire in an aircraft which that person provides...
This distinction even applies to experimental (homebuilt) aircraft. You can't put an experimental aircraft in a training fleet, but if you own one (even one you didn't build), you can, of course, receive (and pay for) instruction in that aircraft.
(The above is one reason I use the Extra 300L for the training and aerobatic rides that I give. It's certificated in the normal, utility, and acrobatic categories and has a standard airworthiness certificate, just like a Cessna 172. Most comparable high-performance aerobatic airplanes--the Edge 540, Sukois, Yaks, et al. are in the experimental category.)
Somewhat similar logic applies to flight instruction. A CFI doesn't need a current medical (see
61.23(b)5) to provide and be compensated for giving flight instruction, provided the pilot receiving the instruction is properly certificated (i.e., holds at least a private pilot certificate), has a valid medical, and is legal to act as PIC (i.e., has a current flight review on the date the instruction is given, has logged 3 takeoffs and landings in the preceding 90 days, and is IFR legal if the flight takes place in IMC, etc.)