You ask:
"What I'm wondering is, are they doing that because they believe it, or are they doing it so they can rhetorically distance themselves from the US?"

Once we pack up and go home, they still have to live in "the region". They absolutely want no part of a war with NATO+ but they don't want to have to keep fighting wars with their neighbors once this thing is over. Iran and Iranians (by their history) are perhaps the most "cosmopolitan" of the Arab nations (along with Iraq and the entire region formerly known as "the Persian Empire"). Recent history aside, these nations have long been major traders with the Europeans (including Romans, Greeks, etc...) and are very used to having foreign influences in their countries.

Simple answer to your question, they are thinking more in terms of "when this thing is over". The Iranians (I believe rightly) believe that they are not in the crosshairs... And if Iraq happens to be... they truly aren't going to care all that much... To answer your question...
[link|http://www.heraldnet.com/Stories/01/10/7/14478787.cfm|http://www.heraldne...14478787.cfm]

"Almost all the merchants, traders and preachers were from the mainstream Sunni branch of Islam, and today most Asian Muslims adhere to Sunni Islam.

Mystics of the Sunni branch, called Sufis, preached widely in Asia and were instrumental in converting people. Sufism, which emphasizes personal devotion and often blends local practices into its worship, is still powerful among Asian Muslims.

The other main branch of Islam, although much smaller, is Shiism, which dominates Iran and is the largest sect in Iraq. Pockets of Shiite Islam also exist in Afghanistan, Pakistan and Tajikistan.

Shiism, originally a dissident faction, has its own distinct rituals and a more organized and hierarchical clerical system than Sunni Islam.

A strict form of Islam called Wahhabism, founded in Saudi Arabia at the start of the 19th century, still flourishes there today and is making inroads in Asia. Based on a literal translation of the Quran, Wahhabism rejects mysticism and any veneration of saints or their tombs. The movement has served as an inspiration for Osama bin Laden."