Okay, I do not claim to be the most knowledgeable member on the board, far from it, however I am one of the most verbose. Despite that shortcoming perhaps I can help.
1. Where are you downloading from?
2. If the file you are downloading is from here please give an example.
3. I have seen that message before or at least messages like it. It is often an ad of some sort, though this may or may not be applicable in your case.
4. A message warning that the file may be copyrighted is different from a message that the file is copyrighted. I say ignore it. In all fairness I ignore potential copyright issues all the time. I claim nor seek any monetary gain from my possible copyright infringements both downloading and sharing with a total absence of malice to any possible copyright holder. I am not saying I am right or wrong in doing so, just that this is what I do.
addendum:
5. It occured to me I may have misunderstood you. Are you saying you were actually prevented from downloading a file? It does not make sense to me to that a maybe violating DMCA error would prevent a download. Most sites will remove a DMCA complaint immediately.