Regarding the admixture, the analysis doesn't indicate the direction. If a Denisovan had offspring with an ancestor of present day Philippinos and the offspring stayed with the humans, that would create exactly the same D-statistics as if the child stayed with the Denisovans.
I think the most believable scenario is that humans migrated through an area that was already inhabited by Neanderthals, some of them had fun with the locals, and the Denisovan is an offspring of such a family. That's much easier to believe than Denisovans, who somehow never left traces in the fossil record, living all over Asia and contributing genes to all present day Melanesians.
[Reich2010] has a single sentence to rule out this scenario: the fossil is a tiny bit too old to be affected by the migrating modern humans. That relies on stratigraphic dating (C14 fails at around 50ka), and that relies on the assurance of the archaeologists that "most of the site was disturbed, but this fossil is from the undisturbed part!" Yeah, right.
As you said, Denisovans, assuming there was ever more than one, and assuming they weren't just Neanderthals, probably swam to the Philippines. Isn't it amazing how much we can learn from a single pinky bone?