The squaretrade (who does 3rd party extended warranties) report was an analysis of several years of data and some 30,000 warranty claims (if you're talking about the same one I read). So the "most reliable brand" was assessed under those constraints. You can make whatever conclusions you want w/r/to that report but I don't think that under those constraints you can establish one brand's reliability over another.
In my experience it's not brands that demonstrate reliability/unreliability, it's individual model lines. For example my Dell 5150 and my Lenovo T61P were both steaming piles of pooh when it came to hardware reliability, and both of those models have had a considerable number of hardware complaints about them. Also a co-worker of mine got a Dell Studio 15 within a month of them coming out and was plagued with hardware problems (averaging once a month), after 2+ years Dell replaced it with the current Studio 15, and it's been trouble-free. I think that as the model line matured, they either had their suppliers adjust their manufacturing processes or changed out problematic hardware for more reliable options.
A goodly chunk of PC laptops are ODM models, meaning HP/Acer/Gateway/Dell/IBM buys the same machine from Clevo/Compal/Wistron/Quanta and then just re-badges it with their chassis/logos. I'd think the reliability rates for the same platform to be about the same regardless of which OEM actually sold it to you, excepting when they demand out-of-spec hardware. Interestingly, I believe ASUS ("most reliable" per the squaretrade paper) actually makes most of their own machines.