It is heavy music. I would probably categorize them as heavy metal. The thing is, a lot of self proclaimed "metalheads" think anyone who doesn't scream constantly isn't a metal musician. Also, the lyrics aren't about destroying the world, the path of satan, ripping the heads off goats, sex with dead bodies, and other "metal" subjects. There are tons of bands that do not sing about those things, but stuff like Cradle of Filth makes the stereotypes more often than more moderate artists do. Disturbed is just quite obviously about all of it's social, religious (not satanist), whatever messages because it's all sung. Quite well, I might add, and you can hear the words perfectly. It doesn't fit in in the modern "metal" scene at all. This isn't bad, just different.
I guess it depends on your definition of "metal". If Opeth is the lightest music you ever listen to, then Disturbed might not seem like metal. But if you listen to a wide range of genres it definitely leans towards the heavy side of things.
Undeniably, it does attract people who have no knowledge of the much larger genre of "metal", who don't know the difference between hardcore and death metal, and who think "superman that ho" is the most ingenious lyric anyone ever came up with... and generally make a fool of themselves trying to talk about what music they listen to. But that doesn't diminish the band's awesomeness.
And damn, that was a long post that didn't make much sense. Sorry if most of it is indecipherable.