Yes ISIS really is Islamic whatever the BBC* and others would have us believe: the "ISIS has nothing to do with Islam" crowd.
*[Later: apparently I'm wrong about the BBC, in that its head of Religious programming, himself a Muslim, has said that ISIS is indeed Islamic. "They're not preaching Judaism", Aaqil Ahmed wisely notes, according to that report. Mind you, I don't trust the site, so will have to double check that one]
This report linked here was done for the Austrian ministry of Foreign Affairs.
A snip from the article quotes Dr Zuhdi Jasser, himself a reforming Muslim:
Dr. M. Zuhdi Jasser, a Muslim and leader of the American Islamic Forum for Democracy, told Lifezette: "This study proves what any honest Muslim already knows or [has] been in major denial about. While our 'Islam' as we practice it here in the West is for reform-minded Muslims compatible with Western values, the reality is the 'Islam' practiced by large swaths of Muslims in Muslim-majority nations run by Shariah law is supremacist and theocratic in mindset."
He continued: "Our organization [AIFD] and other leaders in our Muslim reform movement have been screaming from the rooftops for over a decade that there is a direct connection between non-violent Islamism (the supremacism of Islamic states based in Shariah law) and the violent Islamism of militant jihadists. One naturally leads to the other, and this study is simply proving what has been painfully obvious to any honest Muslims.
"Islamists will blame the 'anti-Muslim bigotry' or aka 'Islamophobia' of the 'right' when in fact it is Islamist groups in the West (Muslim Brotherhood legacy groups) that exaggerate the extent of anti-Muslim bigotry, trying to impose anti-blasphemy behaviors by calling it 'Islamophobia,'" Jasser said. "The Islamist groups like CAIR, MPAC, MAS, ICNA, ISNA and others will do anything possible to blame everyone on the planet who is non-Muslim except their own ideologies and in essence the ideology spread across the planet by OIC [Organization of Islamic Cooperation] regimes of Saudi Arabia, Iran, and Pakistan, to name a few."