This argument is utterly vacuous. "Employment at will" gives employers the freedom to test/fire for anything except for prohibited discrimination. And even those prohibitions should be ruled unconstitutional
The ‘’employment at will’’ clause always ticked me off whenever I worked for an employer who had this stipulation. I turned the tables on one when given the offer of a better job, I just up an quit. The company HR person wanted to know why I hadn’t given ‘’notice’’. I said ‘’At will works two ways’’.