As you've just suggested in the discussion area, at the time of the Los Angeles Olympics in 1984 Moses trained at the University of California at Irvine, just south of Los Angeles. He lived in Laurel Hills, a little further south, but very close. I don't know whether he was formally affiliated to UC Irvine, but I think being based there as an athlete, added to the fact that he lived nearby, is enough to justify saying he was "from" Irvine.

This is from July 30, 1984, the very time of the LA Olympics:

"Another crowd this day keeps its distance. It's made up mostly of female athletes and male oglers gathered for a women's invitational meet on the campus of the University of California at Irvine, Moses's primary training ground. [...]
In winter Moses does endurance work on the soft beaches or on the rolling hills of a golf course near his Laguna Hills condo. [...]
An inviting sun having returned to Southern California this day, Moses is back running on the grass at Irvine."
http://www.si.com/vault/1984/07/30/620185/the-man-who-never-...

This is from an article by Moses himself, referring to 1984:

"In early February I would start reducing the distance, working at the University of California at Irvine. I would run 800m and 400m and the time would be a lot quicker than I was running the month before."
http://www.telegraph.co.uk/sport/olympics/9210009/Edwin-Mose...

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Note added at 1 hr (2016-03-10 06:01:17 GMT)
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I love this quotation from Moses' wife in the first source cited above, referring to the fact that he had such long legs:

"Edwin's advantage is that the other fellas actually have to jump over the hurdles."