Can you fly from Florida to Chicago on airplane if you have a mexican consular id?

My friend is wanting to come visit me from Florida and all she has is a Mexican Consular Id. I told her not to fly out here because it might be a little risky, she said she contacted the TSA and they told her they are not interested in the immigration status of the people flying is that true and if it is then why are there INS officers always at the airport?