Of course the phenomenon is explained by Many Worlds, that's an interpretation of QM that should be consistent with the evidence we have in all cases if it's not to be discarded. Many Worlds is also hardly a persecuted viewpoint, it may not have penetrated into the popular consciousness but I seem to recall evidence that most actual physicists don't use a collapse postulate. I certainly know that my of my physicist friends here in the MIT community everyone holds with some sort of non-collapse interpretation.

EDIT: Wait, I just remembered one dual physics/philosophy major who believes in quantum collapse. But even she thinks that the Copenhagen Interpretation, the one you usually see in the media, is ridiculous.

I'll say that, personally, I find it much easier to make sense of situations involving long range entanglements when I think about them in terms of Many Worlds than when I think about them in terms of waveform collapse. And the term "teleportation" as applied to these results really does annoy me.