This is a good observation, but it is a misinterpretation of causality. There is only one grey gene, and I doubt very much that another will ever be found, there is no reason to believe it will.
What you are seeing is something genetic, yes. But it is not two different grey genes, it is something else - the "fleabitten" code. Just like all bay horses are black based, so all fleabitten greys are grey based, and it's the same gene as non-fleabitten. Just something ELSE aside from that causing the fleabitten pattern.
That's what I was thinking, too. Fleabitten and non-fleabitten grays will both test positive for the DNA tests for gray, so they're the same gene. We're still a long way from fully understanding every gene and what it does, which is why there are lots of color variations that we currently can't explain or test for (what makes some chestnut horses dark and some light?) I'd say it's very likely there's a heritable genetic component to fleabites; we just haven't singled it out yet.