If it were handled the DMCA way, here is how it would go.
1. Someone complains to the hosting service alleging that you are violating their copyright.
2. The hosting provider takes down the material and notifies you. If you do not want to dispute this, that is the end of it.
3. If you want to dispute their claims, you notify the hosting provider. It doesn't really matter, as far as I recall, if you dispute the claims because you say the claimant does not hold copyright, or you say that they do but your use is covered by fair use, or any other mean.
4. The hosting provider puts your material back up, and tells the complainant that if they want to take it down, they need to take you to court, and provides your legal contact information for filing said suit.
If the claimant takes you to court, and wins, following the above procedure absolves the hosting provider of any liability for the infringement.