No, in a word.
One need only look at the JD Power surveys to see this. US manufacturers constantly rank very poorly in the overall reliability stakes, with VAG fair to middling. Mind you, much of that is due to perceptions of reliability (you expect a Mercedes to break less than a Rover, for instance, so the score is skewed by that).
If youc ompare like with like across most of the market sector, US cars are no more mechanically reliable than those from elsewhere. There are some engines or designs that buck this trend (the big V8 engines that have been in production for the best part of half a century in obey form or another, or the utilitarian diesel engines, for instance) but what really ikes me about that quote is the allegation that European providers cut corners when it comes to mechanical engineering. Its a totally absurd fallacy- the R&D budget for even small hatches completely dwarfs that of even the premium US car segment in many cases, and its predominantly European and Asian providers who are pushing the boundaries of mechanical expertise. Fuel stratified injection/direct injection, compound forced induction, twin scroll and variable geometry turbocharging, multiple throttle body setups, flat-plane V engines, viable valve timing and inlet manifold- all were brought to the mass market by European producers.
I suppose how you measure it matters, thought. The US approach to engineering has always been more utilitarian than that in Europe. But to imply that the quality of mechanical engineering in US cars is better than that in European cars is obviously false, and just smacks of self-serving protectionism.