If MS truly felt they were losing money, they'd shut down the links. Bing links are, for obvious reasons, much easier to shut down than Google links. But they didn't. You can do the rest of the computation.
If MS removed those links from Bing, then people might complain that MS is selectively altering search results for its own benefit. (I'm only half-joking.)
So why are they then contracting out the takedown notices to a third party which must be charging them a whole bunch for sending notices for hundreds of thousands of links? Just to make Bing better and Google worse for 0.01% of popular illegal downloads? Again, does not compute.