That's an interesting interpretation, and I'm sure some people do mean it that way, but you have to understand it is not always meant that way, and nor is it interpreted that way by non-believers.
Now, I am perfectly willing to take "Merry Christmas" or any other seasonal greeting in stride, particularly if it's somebody I know and I have no reason to question their motives. But the folks who push the notion of a "War on Christmas" encourage Christians to say "Merry Christmas" specifically
because it agitates against "political correctness" and pisses off those godless atheists.
As a perfect example of what I'm talking about, a member on this very board has this as their avatar:
Tell me, what the hell is inclusive about
that? Bill O'Reilly pointing a gun at you, demanding you say "Christmas." Yeah, no implied coercion or religious oppression there. Even in jest, I don't find it all that amusing. If folks feel like hearing "Happy Holidays" diminishes the meaning of Christmas, well, tough shit. Someone snarling "Merry Christmas" at me because they think they're fighting a "War on Christmas" can get fucked.