Billy Corgan is pretty sure he saw a shapeshifter once 

This comes from Spin, which reports that Corgan said he “was not [on drugs]” and “was totally sober,” and all he knows that he saw someone undergo a “transformation” that he can’t explain. “Imagine you’re doing something and suddenly you turn around and there’s somebody else standing there,” he said, adding that he’d “rather not go into details.” Stern asked if questioned the shapeshifter about why they transformed, and Corgan says he did and “they acknowledged it,” but they wouldn’t say anything about what they were doing.

Basically, Corgan saw a person turn into a totally different person, and when he confronted them about it, they admitted that it did happen but gave him a “don’t worry about it” when he asked why. It would be rude to suggest that he made any of this up, though, so the only possibility is that Corgan really did make contact with some kind of supernatural shapeshifter. That still leaves us in the dark as to what this shapeshifter wanted or why it risked altering it form right in front of Billy Corgan (of all people), but maybe it was preparing for some kind of secret invasion of alien shapeshifters. That could be fun.