Mythbusters

[LunarOrbit]

...Would their tests aboard the "vomit comet" be different if they used someone else's plane?

Are Zero G Corporation (who's flight it was) connected to NASA?

They're a private company, but NASA does use them.

NASA Flight Opportunities Program

NASA depends on advances in technology, and yet, space testing and space qualification of promising technologies remains one of the most difficult of all NASA’s hurdles. High costs and risk of flight demonstration to incorporate advanced technologies into future missions have been a great challenge to NASA. Flying payloads on commercial parabolic aircraft, such as Zero Gravity Corporation’s specially-modified 727-200, named G-FORCE ONE™, and reusable suborbital vehicles will bridge the famed “valley of death” and help move technologies rapidly to maturity.
 
The NASA Flight Opportunities Program intends to mature towards flight readiness status new crosscutting technologies that advance or enable multiple future space missions. To facilitate this goal, NASA is providing access to certain flight opportunities available to the Agency, on a no-exchange-of funds basis, to entities that have technology payloads meeting specified criteria.

[Jason Thompson]

the fact is if you want to put the hoaxers to rest if you can keep nasa out of it and use private sources who dont have that connection the better.

The fact is that you can't put hoaxers to rest. They don't care about reality, they care about promiting their own self image. One of the most prominent, Bill Kaysing, once claimed that such independent verification of the landing sites would convince him that Apollo was real. When he was told that there would be such images soon he changed his story to say that nothing could convince him. He is literally on record changing his criteria for being convinced he was wrong in the space of a minute. And he is not unique.

Hoaxers have not concluded the landings were faked by rational examination of the evidence, therefore there is no way to use evidence to ratioanlly convince them they are incorrect. Many of them don't care.

[Halcyon Dayz, FCD]

For example the standard response to the fact that the Russians agree that Apollo was real is answered by the unsupported claim that the U.S. governmental bought their compliance with a grain shipment agreement that saved the USSR from starvation.  Hoax believers live in their own special world of rationalization not one of empiricism and reason.

1966-1970 was the only time in Soviet Union history that grain production actually matched the 5 year plan. Things were fine.
When I ask any hoaxie who makes such a claim how the Soviet leadership could have known then that things would be so bad in the 70s I get no response.

As I keep saying the hoax is only possible if the conspirators had a time machine.