As I explained on your other thread, we do not operate a 'name and shame' policy on these forums. We're more than happy to (politely and respectfully) discuss design features that irritate the heck out of you, but we're not in the business of setting out to damage a company's reputation.
There are some advantages of using grey text over black ... particularly if you go for a dark charcoal shade rather than a light silver shade – it can make text easier to read, particularly for people with dyslexia, and it can appear less threatening than the starkness of black against white.
On the other hand, I do completely agree that too many sites go for what they perceive as a trendy route, with the greys far too pale to be read easily.
Part of the problem is the different people see a page in different contexts. The age and quality of your monitor plays a role. The ambient lighting around you plays a role. Whether you have any form of anti-aliasing or sub-pixel hinting plays a role. And that's before you even get down to the question of an individual's eyesight, which can create huge problems for some people reading text that has insufficient contrast.
If designers are used to seeing text render crisply and cleanly on a high quality screen in perfect light conditions, and have 20:20 vision themselves, it needs quite a lot of empathy to come to terms with the need to use dark text. Why do designers dislike dark text so much? Because a lot of them see text as simply another design element to be manipulated in search of improved aesthetics. Black or very dark text can dominate a page's appearance at the expense of the design features that they have put most of their effort into, so they try to soften it so that the graphics come to the fore.
I'm not saying that all designers are like that – not by a long way. Just that there is a significant minority who have a tendency to put aesthetics ahead of practicality.