My experience has been a little different.
First was a cracked Santa Cruz swingarm. I called them up and described the problem. They were very apologetic: "Oh... yeah... sorry. We don't have any of those right now. It will be a couple weeks until we get them back from powder coating. But if you want any other color, we can ship it tomorrow." I didn't care about color, and my bike was back up and running by the end of the week.
The other was a Specialized. Again, it was a cracked swingarm. The bike was a couple years old, and it was purchased second hand. Despite the lack of official paperwork, Specialized sent out a new swingarm in a few days. As it turned out, there were two versions, and this one didn't fit the bike. Unfortunately, they didn't have any correct swingarms left. It was too old. Bummer/ But after a few days, their customer service guy went out to the warehouse and found one of their factory test bikes with the correct swingarm. They disassembled it and sent out the correct part. Even though the part wasn't new, the bike was back up and running, and it took less than two weeks.
Once again, buy only from companies that have a strong presence in your area.