My take on BB and staff's defensive philosophy is: Do vanilla/the basics consistently satisfactory (the target is: never give up too many big plays/never give up easy TDs). Do that consistently well and We'll expand outside the vanilla scheme.
If that philosophy is true then has the defense instilled that kind of confidence in BB/MP/Staff?
As far as BB acting without consultation/unilaterally on Collins is something I don't buy. I'd be shocked if he called MP into his office to say "I'm unhappy with the D Matt so I'm trading one of your stars. I hope that delivers a clear message to you Matt!". That kind of action just doesn't mesh with my understanding of how BB operates. I'd bet the mortgage BB and JM and other D staff have been watching film and had (rightly or wrongly) identified Collins recent(or longer) play as problematic. I'd bet the farm MP has been reviewing the film, has been working to rectify what he/they've been seeing on film regarding Collins, and he ultimately to some degree bought off on getting rid of Collins due to it not improving. And if that's not the case I'm surprised BB and MP have remained together after several years now (and this may just be MP's last season under BB).
As far as Collins, the trade may be the best thing that has happened for him. There are D philosophies out there that value free lancing, attacking style. Maybe he'll thrive again under that kind of scheme. For me, personally, while I'd love to see our D be good enough to attack!, it's not optimal for our current team. Gronk, Bennett, Blount, Jules, DA, Hogan, White, Lewis, BRADY - the sky is the limit with our O. Give us a D that makes opposing offenses earn every point and IMHO that is a solid scheme to the fifth ring.