Earlier quoted context omitted.
On the Apple Support page here: https://support.apple.com/en-in/102174 In the screenshot it says the threat notification was sent "via email and iMessage", so it would not be displayed in any different way on your phone, which I also find surprising. I definitely wouldn't expect to receive something like this as an Email, and I have turned off iMessage.
Just out of curiosity why would you have imessage turned off?
imessage and rcs (and arguably mms, although that started as cost cutting) are backdoors for the legal protections on mining telephony provider metadata for marketing. with those two "opt in" (lol) techs, all safeguards are off.