So, there were transient failures coming from trying to check each of all three links, and I couldn't hunt up the problem - I suspect some kind of race condition somewhere in the Travis infrastructure. But, I realized that if we can load one video, we can load any video for which we actually have the assets. Running this test in a loop doesn't add security, it just checks the completeness of the fixture set, which we already know is a bit dodgy and have a separate ticket (#2183) to fix.

So, I just picked one video arbitrarily and checked it. The transient failures went away.