Clearly no correlation. I do not get better when I get off my flash bike and climb onto my Carrera. And I'm a better rider now than when I only had that Carrera.
Why would anyone believe there's any connection? Some folks will believe anything.
That's the interesting thing about life, people have different experiences. I happen to know a few brilliant riders who ride pretty average bikes, as they seem more interested in riding than collecting anodized trinkets for their bikes.
I have also met and know quite a few guys who spend months building bikes that are dripping with matching chris king, team green hope and any other shiny expensive bling bit you care to mention. The are not great at riding (hardly ride at all in fact) and the spend more time lusting and collecting shiny things, rather than using their bikes.
Now I have no idea whether this is the norm, hence me asking the question. I do not care either way (although I do find it a bit odd collecting shiny things and not using them or perhaps expecting them to make you go faster) Maybe I happen to know some very strange people who are magpies, or perhaps collecting shiny bits to build the ultimate bike and then not actually riding it is a fairly common thing?
I personally couldn't care less if someone has a ten grand mtb and rides it on the road, as long as they are enjoying themselves. Buying an expensive bike and then using it as an excuse because it doesn't have the latest bit of go faster bells and whistles, or not actually riding it at all is not something I understand.