They can take any position they want .... but it's not likely that the labor board will agree with them.
Early in the days of high tech replacements for the old-fashioned time card, I worked one place where we swiped a 'credit card' through the reader. Well, Murphy reported for work along with me, on my first day .....
I would come to work, and clock in. Another employee would come in .. and his card swipe would both clock him in, and me out. At day's end, his swipe would clock him out, and me in ... until I clocked out a few minutes later. So, payroll thought I worked 5 minutes in the morning, and 5 minutes in the afternoon.
Not possible? That's what all the experts said ... until they were able to do it themselves. Perhaps there was but a one in a gazillion chance of the cards being so coded ... but there was still that one chance!
I dislike the product you mention, simply because their advertising seems to presume that the employee is busy cheating the employer. As someone who likes to consider himself a professional, I have little patience for chair-borne commandos frittering away the money I earn for them, doubting my dedication.
If they're not willing to fix it, it's time to fire them. Find another contractor.