So you are advocating the replacement of a part that is working absolutely fine, on the premise that it "might" give problems later? Sorry man, but lifes too short to be scared all the time, worrying about what might happen.
If its working fine now, then run with it. What would happen if you replaced a perfect functioning PSU (albeit with a bad reputation) and the replacement ends up giving you problems? It could happen, just as your tyre situation could happen.
Also consider that around the world, most of the computers are OEM builds. And these OEM built PCs invariably use cheapo PSUs (try opening up a DELL and see what they use). The reason why OEM companies use these PSUs are because they are cost effective. If they found that they were creating problems (especially during the warranty period), they would be losing too much money on replacing the PSUs (and any components damaged), they would eventually realise that it isnt worth saving pennies on a cheap PSUs as later on, it comes back to bite you in the backside. This clearly has not happened. We can therefore assume that it is safe to use the cheaper PSUs, once the PSU is up and running fine.
I think enthusiast sites like this have scaremongered people into buying very expensive, over powered PSUs that are not actually necessary. The only people who win are the PSU makers and their bank accounts.