This isn’t really the truth. In some cases a studio will ask multiple shops to cut on a film, however in many cases you as the editor will cut the trailer and that will be what’s finished. In some cases the individual trailer house might have multiple editors on the job so that the client gets options, but because trailers cost so much to make they often pick a trailer house and stick with them unless they really screw things up.
Just like many of the other posters have said, trailer editing isn’t easy to get into, especially if you desire to work on theatrical domestic trailers (the cream of the crop in the trailer world). I would suggest that you put together the best reel you can, perhaps with some spec trailers (you can digitize your favorate film and use that to cut a version of a trailer) and get that out to everybody and anybody. most likely you will be up for an assistant position and if you do get one (these are also very hard to get in LA) then i would work your ass off and learn as much as you can from everybody around you. Trailer editing while a group activity to some degree is still all about the editor sitting in a dark room alone and cutting. Any good producer who’s got work on their table doesn’t have the time to babysit an editor and that’s why the best are paid well because they are trusted.
Good luck.
jason