Anything is possible if you deem it such. Lots of psychics in real life can communicate with the dead, so I don't see why it would be impossible to communicate with DD from beyond the grave. I rather expected DD to reveal whatever reason he had for Trusting Snape, at that moment. I thought maybe Snape underwent some sort of magic to force his loyalty DD.

Perhaps DD saved his life? Maybe that's why DD thought he could trust Snape? In fact I'll bet that's what the case was. DD saved his life a long time ago creating an impenitrable magical bond between the two forcing Snape to save DDs life at the first possible moment and that's why DD thought he could trust him. Rather similar to Pettigrew's debt to Harry and Snape's debt to Harry's father. The only reason that Snape killed DD was because he saved his life once when he rescued him from the horcrux ring so snape's debt was paid and he became free to make the unbreakable vow to kill DD. DD having enjoyed so many years of Snape's loyalty preffered to think that Snape had come over to the good guys in spirit and by deed. Maybe by deed, but not in heart or spirit.

Just my thoughts on why Snape betrayed DD. Yours?