My answer follows, but if you know better, drop us a line in the comments.
I am not familiar with Grey Pearmain, and in any case people call their apples all different things, not always correctly. But on balance it does not seem likely that these are the same.
True, Google finds several references for "Grey Pearmain" suggesting it may be the same apple as Pomme Gris (Grise). On closer inspection these all turn out to be the same reference, an email or chat-board message from Claude in Quebec:
Could this Grey Pearmain be the Pomme grise? Among its synonyms, there is Gray Apple and Reinette grise. Sometimes, the Reinettes' names are translated as Pearmains in English. The description you give could fit for Pomme grise.
On the other hand, googling "Gray Pearmain", with an a, finds many more references, suggesting that "gray" is the correct spelling.
Among those references, this striking photograph of three Gray Pearmain apples does not resemble Pomme Gris--there's very little russet, though that is not conclusive.
However, one nursery sells scionwood for both varieties, which barring outright error suggests that Pomme Gris cannot be the same as Gray Pearmain.
Still, errors are possible. One orchard suggests that Gray Pearmain may be Reinette Grise De La Creuse, which dates from about 1950 according to the UK National Fruit Collection. However, the Gray Pearmain was known in Maine at least as early as 1885.
Update: The true Gray Pearmain is here.