Not exactly true. Just because it's someone else's plane doesn't by itself make it legal to "accept compensation in all (direct and indirect forms)." You may accept compensation only from the person who controls the plane and only for your pilot services, and not from someone other than the party who procured the plane who is paying only to be flown somewhere.
No, it doesn't, as you note below:
The FAA Chief Counsel's office was very clear about how this has to be done in an
official letter on the subject back in 1990.
You cannot do the renting in this case; it must be done by and paid directly by the company, not you.