Nope, your identity theft paradigm fell apart again. What happened was that DHS sent out roughly 100,000 of these emails en masse. They got the email addresses from forms the aliens had filed with INS. On those forms were contact information, which in many cases included email addresses, for the alien's lawyer(s) as well as for medical professionals for aliens that were undergoing medical treatment in the US. DHS evidently allowed AI to extract all email addresses from the scanned forms without any human review.
So again, incompetence on the part of DHS. They weren't even smart enough to separate out the names and email addresses of aliens from those of associated contacts.
See
here:
Make stupid excuses and you end up looking stupid yourself; not that it takes much for you because you're just pulling excuses out of your ass.