Actually, it'd be pretty easy for this game to be exclusive.

Step 1) Activision has no interest or desire in investing and developing a new Crash game

Step 2) Sony has a great deal of interest and offers to fund development or, have one of their studios develope the title

Step 3)  That's it, there are no other steps.  The game would be exclusive.

I mean, is that likely?  Who knows, Sony seems pretty intent on raising the hype for such a thing.  Layton's shirt can't just have been a troll last year.  Virtually everything they do at these events is for a reason.

Well Sony has shown us in the last couple of years that they have a very good partnership with Activision (Destiny deal, Call of Duty deal...). So it is possible that they asked Activision to develop an exclusive Crash Bandicoot for Playstation 4 by one of Sony's studios (and in the end Sony and Activision share the profit). Someone also mentioned that there are also rumors that Sony is releasing an exclusive Spiderman on Playstation 4 though all the Spiderman game rights are owned by Acitivsion. So it definitely seems likely that Sony has a deal with Activision. There are just too many hints that Crash Bandicoot will come back.

There is also a possibility that he is lying because they want to surprise us at E3.
Hope never dies!!!

Give it up already .There will be no new crash game. Never.