When most people ask for snake, they want solid snake.
If he'd said one of the other snakes or implied he meant one? as I said those weren't denied.
To be fair, Big Boss is the only other Snake who is addressed as just "Snake" most of the time. Liquid and Solidus go by the first part of their codenames.
I would've loved Snake a couple patches ago, but Emmit and Isaac have already been added. I know it sounds redundant as a lot of people have already said this, but it's true. There are already enough gun/grenade characters as is. Plus, Snake would be a stealth character and we already have Sly, who alone gets on my nerves. The only characters I think this game should add are Crash and Spyro. Possibly Cloud, but he's a bit more debatable.
I don't think Snake should be in this game either. If they do use him, wouldn't they use "Solid" Snake? As much as I like him, he would be "old" and "slow" for my tastes. Raiden on the other hand is perfect because he is fast and agile with the other characters.