After much digging, I as never able to confirm that Melissa Hodgman actually worked at Milbank, Tweed, Hadley & McCloy.
There is no mention of her anywhere on their website (even among the 'previous associates') and I was not able to find a single case that she worked on.
Now, all this doesn't mean she -didn't- work there, I could just not find any corroboration of it other than a mention on the SEC website.