The OneTimeOnly applies to the insurance, its actually One Insured Time Only.

This is another example of AMA hq putting forth that no -nonmembers can fly at local clubs,
yet in other threads we see that is not actually the case. AMA has plenty of text worded to make folks believe that non-members cannot fly at local club fields, but we have seen them slip up elsewhere and have text that shows they can.

The One Insured Time Only is so the rookie will be insured with AMA pilot insurance,
but any additional times after that he will simply not have AMA pilot insurance,
unless he 'joins' AMA in one way or another (such as Intro Pilot)