You know this is one of those things that sounds terribly hypocritical but in a massive company can easily be just the right hand not knowing what the left hand is doing. Its hard for me to see this as anything more then typical large co bureaucracy.
I'm not following...there aren't 2 parties. There's 1 party, the people sending a take down notice. The question is why aren't they sending the same take down notices to all search engines which have the material in question?
This is interesting though, when I saw the headline about Microsoft making so many takedown requests to Google I assumed the items to be taken down were found by the Bing team, but it seems that isn't the case.