Etymology answer
The OED reveals, as far as we can tell, that Islam is cognate with salaam but not actually derived from it; their common ancestor is salama, which the OED defines as meaning "he was or became safe, secure, or free." Muslim also derives from that word. Thanks for the info, Wendy S.!
As Wendy suggests, I would guess that the range of meanings given for these and related words in Arabic indicates that any sort of statement to the effect that Islam is derived from the word for "peace" is kinda suspect.
More generally, I think it's important not to fall into the "language X uses the same word for concepts Y and Z, so speakers of X must think Y and Z are the same thing" trap. In English, it's pretty clear (to English speakers) that a given word can have a wide range of meanings. Goofy example off the top of my head, 'cause I'm in a rush: to cleave means both to hold onto and to cut in half; that doesn't mean that English speakers believe those two actions are the same thing.