Finally, in a new story from the New York Times, we got the final word on the subject. In an email, Swinton admitted that yes, that is her. The semantics of the situation were this: everyone was asking if she played the old man in Suspiria, but she maintains Lutz Ebersdorf played the character. However, Tilda confirms that she played Lutz Ebersdorf. I know, I know. But, I mean, that's the most Tilda Swinton way to say, "Yes, that's me under all those prosthetics." Now we can rest easy.
As an added bonus, I hope you take solace knowing that Tilda had fake male genitalia made for the whole affair. I'm shook.