Thank you for your question.
It has certainly stirred up a lot of controversy. The Sunnah (authentic sayings of Prophet Muhammad) is very clear on the issue regarding making pictures of humans or any other animate beings. It is not permissible. Islam was sent to do away with the practices of people worshiping the creation and solely focusing their worship to the Creator alone. Creating images and statues of people is at the root of idolatry, which Islam is completely against.
Any depiction of the prophets, not just Muhammad, but of Jesus, Moses, etc.. is not permissible.
This is not a new concept. One of the ten commandments from the Bible says:
“You shall not make for yourself a carved image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth."
So as Muslims, we take offense to any depiction of the prophets. Whether they draw pictures of Muhammad or depict Jesus in offensive cartoons.
So your Muslim co-worker was incorrect when he said that there would be instances where it would be disgraceful to NOT show pictures of him. Any depiction of any of the prophets is not permissible.
Also, the way we Muslims reacted to this by rioting and violence is also not permissible, but I guess that is for another question..