There's no law saying they can't turn all American infants into catfood either.

Congress mandates action by the USG. The Executive carries it out, and the Judiciary keeps their leashes short. Given the specific prohibition on even abridging the speech of Americans permitted Congressional mandate, it is a logical fallacy to suppose that the Executive can just do whatever it wants outside of a mandate from Congress, particularly to take actions specifically prohibited Congressional mandate.

It's treason. Whoever made the claim that the Executive can act absent a mandate by Congress is an apologist for tyranny.