Edit: Shit, meant to edit this into my last post. Oops. >.<
You seriously think Sony has any say over what Activision does with their games??
Activision would not want BC because it would possibly eat into their profits for future COD games. They want people upgrading not playing older and more beloved versions.
But I mean, people can already continue playing those older versions if they really want to, and making it hard to play older games isn't going to make them more likely to buy newer ones. They're just making things more inconvenient for their own fans. Plus, making them available on Xbox One means they can continue promote those old games on a new marketplace and get more sales out of them.
I'm not going to pretend like I know what's going on with Activision, but they can be really weird about stuff sometimes, and often they just don't seem to care. Remember how long it took them to support the Wii U eShop? It was like, years, with no real reason what-so-ever for holding out. I don't think they're genuinely that worried about old games cannibalizing the sales of new ones. They're just backwards about some stuff like this, and it doesn't really matter to them since they'll make a fortune on the next Destiny, CoD, and Skylanders releases anyway.