The myth is this: every time the PTR goes up, my server slows down.
I play mainly in two different servers, Anvilmar and Eldre'Thalas. I've heard it claimed often enough on both servers that the PTR seriously effects stability. Most people claim this is because the PTR and the server hardware are on the same "rack." Most servers are just a small gray box with a few blinking lights on the front of them, and lots of connection ports in the back. When making a server farm, like Blizzard has scattered throughout the country, they physically put the servers in clusters, called racks (no, not that kind of cluster, well kind of, but that's beside the point).
Today Hortus has dispelled the myth. The PTR servers are on a separate rack from any live servers. So it's just a coincidence that we're having all these connectivity issues, right?
While it's nice to know that the servers are at least physically separate from one another (not that it matters much in the first place), we can reasonably assume that the PTR is at least housed in the same complex as some live servers. This means that no matter what, the data center where the PTR servers are housed will see increased traffic. While we like to think of bandwidth as an unlimited commodity, if even 10% of the World of Warcraft user base wants to get on the PTR, that's still a million new people traveling to that data center, which will lead to decreased speed throughout. So perhaps this isn't a coincidence after all? Could this explain all these server issues as of late?
So at least the myth of the server rack space has been busted. What remains is to find out which servers are in the same data center as the PTR. Then we'll really know which servers to roll alts on when the PTR hits.
Have you noticed your server failing since the PTR hit? Give details, like what server you're on, what battle group, and what time zone.
Updated 2:53 p.m. EST: Jasperwind provided a great link to a WoWWiki article that shows the PTR is in the LA data center.