As I am fond of pointing out, any non-Muslim who asserts that "Islam is a religion of peace" is a deluded fool, but strangely a Muslim who asserts "Islam is a religion of peace," is not lying. Rather he is showing that the Islamic concept of peace is severely defective.
In Semitic languages, the consonant sequence is the root of the word, thus Islam (submission) and Salam (peace) both have the root SLM. In the Muslim mind, peace and submission are inextricably linked. No permanent peace treaty with non-Muslims, binding on Muslims, can be concluded, only hudna (pauses) which can be abrogated at will by the Muslims if it is to their advantage, without any moral qualms about having been dishonest. There is no equivalent of "the peace of God which passes all understanding" in Islam -- the Islamic conception of heaven is sensual and materialistic, with watching the torments of the damned as one of the entertainments. The only peace Islam knows or offers is the peace between conqueror and conquered, between master and submissive slave. So, yes, they can say "Islam is a religion of peace" with a straight-face, and without lying, but it is the religion of the "peace" I just described not of what Christians, Jews, Buddhists, Hindus, Sikhs, or secularists from cultures deriving from any of those traditions mean by "peace".