If this individual makes it known to the owner and an agreement is in place prior to him stepping foot into that aircraft that should something go wrong, he is not at the controls, etc, then by no means would he be deemed the PIC of the owner furnished aircraft.
Not true. The FAA has ruled many times that a CFI is PIC even if that CFI is
not in the front seat and does
not have access to the flight controls. The remedial training programs, 709 rides, and so on don't make it to the online court cases. Besides, can most CFIs afford an NTSB appeal? Can their estate?
Each owner should check their insurance and add you as additional insured to their policy if you do not qualify under "open pilot" or "open instructor" clauses. Make sure you are covered as an instructor, not just a pilot. When something goes wrong, the insurance company will look for any excuse not to pay. They may deem you PIC even if the FAA has not done so.
Finally, why would you want to instruct and not be PIC? Especially when you'll be instructing folks that are not confident of their ability in conditions where they are not confident? Make it easy on all and just be PIC.
Set expectations up front. 1. Airworthy aircraft including all supplements to the flight manual (new avionics, engine upgrades, etc). 2. You're insured. 3. You are PIC and will keep that right. 4. Even if the pilot thinks they know the plane better than you, you are still the instructor, otherwise, why are you there? 5. Get a copy of the checklists and make your own version. 6. In multi's you'll need 5 hours of PIC before you can instruct. 7. In others, the first flight will be VFR in VFR so you can get familiar with the plane.
There will be many times where you will have to check yourself out as a CFI. Why pass up the opportunity to fly several unique, well-equipped, well-maintained aircraft when with a little study and a flight you can be up to speed?
Those owners that happily accept your boundaries are worth flying with and will probably greatly benefit from your instruction. They may even thank you for helping them bring their airplane into compliance. They may hire you to manage their plane or be their corporate pilot (be familiar with part 119/135 and don't stray into it). Those that won't accept your limits, are not, will not, and won't. Why waste your time with those types?
I fly a lot of spotless Bonanzas, 210s, Dakotas, and other unique airplanes with plenty of toys in the panel. I haven't flown or needed to fly a junker (airworthy but, no moving map GPS, working autopilot, GEM/JPI, and so on) since April.
While your co-irkers are bouncing around the pattern in the school's planes, you'll be flying cross countries in Bonanzas, 210s, Saratogas, and probably a whole host of twins.
Fly SAFE!
Jedi Nein
