I agree with you Lady Radagu! I posit that David's power is copying powers from epics that he touches. He touches Prof, and gets unusually strong healing powers. He grabs Obliteration, and he later is teleported out of a life-threatening Prof-bubble right before Megan's entrance.
Although Megan could have "dimensionally swapped" David out of the bubble, I don't think she's ever shown ability to move people, and earlier she was afraid to mess with David's face, so why would she now swap his entire being? And if she could move people, why not dimensionally swap herself immediately into the fight, or swap Prof really far away?
Also, it has been hinted several times that David has a real talent for adopting gifted powers (e.g. the tensors and the water jet pack). And Epics seem to manifest powers related to their past, so David's obsession with collecting data on Epics' powers has now been translated into actually collecting Epics' powers.
But either way, I can't wait for book 3 to find out what happens (which will undoubtedly surprise all of us).