Not just the teachings, but the interpretation itself is also part of the problem. There are some tolerant sects of Islam, such as Sufism and Alawism. But the other sects consider them as heretics, and accuse them of misinterpreting the Islamic teachings.
Yes, they certainly do deny it.
Ridiculous as it may seem.
One major bone of contention in American politics recently was Obama and then Hillary Clinton refusing to use the phrase "Radical Islamic Terrorists," while various Republicans (but not all) argued that it was necessary to name the enemy,to defeat the enemy.
There certainly are other examples, including numerous remarks on this board by Muslims.
What they try to do is arbitrarily exclude the terrorists from the cateory of "Islam" by their own personal decree. It would be pretty funny if it wasn't so serious. It's like someone trying to exclude potatoe from the category of vegetable.