Those quotes are correct. The problem is that taking them like that completely ignores their context. For example, take by far the most widely known verse advocating such things, known as ayat al-sayf, or the Sword Verse:
"So when the sacred months have passed away, then slay the idolaters wherever you find them, and take them captives and besiege them and lie in wait for them in every ambush, then if they repent and keep up prayer and pay the poor-rate, leave their way free to them; surely Allah is Forgiving, Merciful."
The context of this is a war that Muhammad and his followers are waging against a hostile pagan Arab tribe in Mecca (while Muhammad himself is in Medina, where he escaped from Mecca due to persecution). There was a truce in effect at that time, but it was violated by the Meccans, and Muhammad gave them four months to make amends, or else hostilities would be resumed.
Now, most Muslims today interpret this quote in that context - that it was a specific commandment given to the followers within the boundaries set by that particular conflict, and that it ceased to be relevant afterwards. Some - in particular, Salafi - interpret it the way you did, by saying that the context doesn't matter, and that the commandment is generic and applies to the entire Ummah from there on.
The governments are, in fact, fighting the propaganda war - for example, make the state-approved Islamic authorities condemn such interpretations, and issue fatwas against following them.