Maintenance topics often get emotive. But I'd like to point out 2 things.
Firstly, there is a wide range of competence & workmanship that exists by both LAME's & pilot / owners. LAME's are not automatically more skilled (typically - yes. Automatically no). Some owners are highly competent. And there are some jobs that owners do better because they just put much more time into the job that a commercial mechanic wants - or can justify.
Secondly, all the owners that I know who work on their aircraft do it in concert with their LAME. Its not a mutually exclusive thing.
At the end of the day, the real test should be what is the best, rational course of action rather than trying to read nuances into legalese. The LAME's that I respect welcome owner engagement - they typically only get to look at the aircraft for a handful of hours every year. An owner who is familiar with the aircraft and the state of various components who has a strong working relationship with a LAME delivers the best outcome for the aircraft in my opinion.
If a guy wants to change a tyre - good on him. If it means it gets replaced earlier rather than being extended to be done at a 100 hourly, then its a safer choice. While he's there its likely that he'll look look at a bunch of other stuff and gain a better understanding of his aircraft. If this results in more things being brought to the LAME's attention and being fixed then it also leads to a safer aircraft.