Nothing in the notice means that BMF made a claim against this video in particular (in fact, it sounds like it's a private video, so there's no way BMF could review it). It's not a DMCA issue at all -- this is a system that YouTube chose to put in place completely unconnected to any DMCA claim system.
Sounds like this automated scanner result is wrong. I believe there is an appeal process, where a human will look at the video. Also note that the video is not being blocked in the meantime; it's still available.
The bigger problem that comes up is how can YouTube deal with the flood of video copycats (ever notice how every popular video leads to 20 copies of the same thing?) without stifling independent artists whose work gets a false positive in the scan system? It's an interesting challenge to get the right mix of false positives and negatives.
Please post what happens after you try the appeals process -- this could be a simple fix and I'd be curious to know.
Edit: Here's an overview of the automated "Content ID" system: http://www.youtube.com/t/contentid