(My emphasis)The cooperation can come from an understanding of the tool -the DFMEA- or by pressure from management.
To me, that spells out fear, and in my experience not much good normally comes out of that. Yes, it would look like cooperation, but more likely it would be just going through the motions, just to get through and be done with it. FMEAs tend to be resource hungry - a group of highly-paid professionals sitting in a room for a significant number of hours (maybe on multiple occasions). That would be a silly waste of resources just for the sake of appearance.
That's exactly why it does matter who owns it and whether the design team buys in or not. Unless of course you want to police them all the way through...will the outputs of the dfmea lead to an improvement in the design verification and validation or will they sit forgotten in a file that no one will look at?