As I've read more about this issue, I've become more and more skeptical of this claim. I found, for example, this question posted to Ali al-Sistani, a powerful Shi'ite Imam in Iraq:
The answer, according to the Imam, is:
Is it permissible to draw or produce a scene which shows the Prophet Muhammad (s.a.w.), one of the past prophets or the infallible Imams (a.s.), or other luminaries and show it in cinema, on television or theatre?
If due deference and respect is observed, and the scene does not contain anything that would detract from their holy pictures in the minds [of the viewers], there is no problem.
So, at least some Muslims don't subscribe to the "no pictures rule." From what I can gather, it's more or less a Sunni rule and generally not adhered to by the Shi'ites. I've heard you can even buy pictures of Mohammed on the streets of that free-for-all of moral decadence known as Tehran. There are a lot of what are represented as Persian and Afghani depictions of Mohammed here. To characterize what is in reality a Sunni rule as a sacred universal rule of Islam is either misinformed or simply dishonest. Further, to the extent the "no pictures rule" is subscribed to by certain Muslims, it isn't specific to Mohammed alone, but applies to all living things, including "the prophets." Thus, a picture of Jesus or Moses is also forbidden to the devout fundamentalist Sunni. So, why no protests over pictures of the "prophet" Jesus?