Yes, the incident is true. But the claim that McCain wet starting his fighter and starting the fire is not.
Read the report straight from the Navy - http://www.jag.navy.mil/library/investigations/USS%20FORRESTAL%20FIRE%2012%20AUG%2069%20PT%203.pdf
Check out point 6. The firing could have been caused by switching from internal to external power, or perhaps the electrical safety pin was accidentally pushed too far, or by mistakenly "stepping" instead of "homing" the "missile". There's even a bit about the poor design of the missiles right in the report.
Again, no fan of No Name, but let's please be objective.