Consider part 43, appendix A: It is legal for an owner to change a worn out tire. It's also legal to service wheel bearings. If, however, in the course of reassembly a new brake rotor or pads are installed instead of the old ones, illegal work has been performed. Part 43 also says nothing of actually inflating tires, so it's unclear— in the letter of the law— whether or not filling flat tires is approved.

There's probably an advisory circular around somewhere that expounds on this, but it illustrates well the over regulated[0] nature of GA in America[1] where the results of regulation do not necessarily effect safety. We have 50 year old (on average) airframes flying around with engines designed in the 1940s (on leaded fuel, no less). It costs $40,000+ to rebuild these engines, due largely to laws about who can work on them and the monopolies on who can provide which engines. It's only like this because the FAA is, for whatever reason, unable to work to a real solution.

[0] This is a specific complaint, not an argument for a general rollback

[1] Yes, I am aware that aviation is even more regulated elsewhere-- and that costs are increased while participation is decreased in those places