Is Islam really a religion of peace?

Now, I am not an expert on any religion, but the refrain that we often hear is "Islam is a peaceful religion".  And it does not want to hurt anyone who is not a Muslim.  Is it?  Here is an incident that happened in presence of the Prophet and was done by one of his top lieutenant.  It does gross one out!  What do you think?  Read this and then the killings of Jews, the torturing of Muslims away from Islam etc will make sense!

Abu Musa said, "I came to the Prophet along with two men (from the tribe) of Ash’ariyin, one on my right and the other on my left, while Allah’s Apostle was brushing his teeth (with a Siwak), and both men asked him for some employment. The Prophet said, ‘O Abu Musa (O ‘Abdullah bin Qais!).’ I said, ‘By Him Who sent you with the Truth, these two men did not tell me what was in their hearts and I did not feel (realize) that they were seeking employment.’ As if I were looking now at his Siwak being drawn to a corner under his lips, and he said, ‘We never (or, we do not) appoint for our affairs anyone who seeks to be employed. But O Abu Musa! (or ‘Abdullah bin Qais!) Go to Yemen.’"

The Prophet then sent Mu’adh bin Jabal after him and when Mu’adh reached him, he spread out a cushion for him and requested him to get down (and sit on the cushion). Behold: There was a fettered man beside Abu Muisa. Mu’adh asked, "Who is this (man)?" Abu Muisa said, "He was a Jew and became a Muslim and then reverted back to Judaism."

Then Abu Muisa requested Mu’adh to sit down but Mu’adh said, "I will not sit down till he has been killed. This is the judgment of Allah and His Apostle (for such cases) and repeated it thrice. Then Abu Musa ordered that the man be killed, and he was killed. Abu Musa added, "Then we discussed the night prayers and one of us said, ‘I pray and sleep, and I hope that Allah will reward me for my sleep as well as for my prayers.’"