imutter could be software related(not saying it is, but possible). Have you tried restoring the device as new and then recording the video? I know that it's tough for something like this to restore as new and see if it fixed it, since it doesn't happen all the time, but it's something that would need to be tried out before Apple would replace it.
Unless you go to an Apple Store that is, over the phone I wouldn't replace it(if I were the over the phone support rep you got) based on it happening sometimes unless it happens after a restore as new. However, if you go to an ARS, they probably would replace it no questions asked, since they have stock available to exchange right then and there.