I would personally adhere to the DMCA notices. Lets say, worst case scenario, you end up in court for facilitating copyright infringement, you have a much better defence having removed content being brought to your attention.

I personally have a system in place so if a post is deleted for whatever reason (dmca notices, etc), the member is automatically notified about it via pm, with it including the contents of the original post. You've done what you're legally obliged to do and the member can repost it if they want .