DMCA notices are issued by the entity which owns the copyrights to the material in question. While it could be a report by someone to the copyright holder, what is more likely is that a company came along, saw something that belongs to them, and issued the DMCA notice to the webmaster. While the ISP can disregard the DMCA notice, they do so at their own peril as penalties can be levied against them in court. The "Safe Harbor" provisions of the DMCA provide an ISP with an alternative to just being taken to court - take the offending material down and have a nice day.
I'll be curious to see if they provide me with information as to what the material in question was. My guess is probably a small-name porn company or somesuch. Most everything else there is covered by fair-use provisions of copyright law.