Update: the Eight Circuit has just upheld a ban in Iowa on using deception to gain employment in order to cause economic harm to the employer. So my guess is these investigations are illegal now, at least in Iowa.
At least harder. One loophole for these kinds of laws is that the intent to deceive has to be there at the time the false employment statement was made. As a commenter on the linked post noted by analogy, loan fraud exists when you never intended to repay, not when you decided not to after getting the loan.
Update: the Eight Circuit has just upheld a ban in Iowa on using deception to gain employment in order to cause economic harm to the employer. So my guess is these investigations are illegal now, at least in Iowa.
At least harder. One loophole for these kinds of laws is that the intent to deceive has to be there at the time the false employment statement was made. As a commenter on the linked post noted by analogy, loan fraud exists when you never intended to repay, not when you decided not to after getting the loan.