Management takes away employee's sick day if they're 1 minute late for 4 shifts; 'Is this legal?'

I am not someone who is cool when people are late all the time. My time on this earth is valuable, and I don't appreciate having to wait for 20 minutes outside of a restaurant in the cold because my friend's "train" was "late." At the same time, I'm not a wholly unreasonable person. I know that being late can often be outside of somebody's control. I also know very well that there's a vast difference between being 1-5 minutes late to something and being 10+ minutes late, especially in the workplace. 

One job clearly didn't know this difference and decided to punish all of their late employees equally. In a bizarre memo that appears to not be proofread in the least, the management of an unknown company told employees that if they were even one minute late for four shifts, one of their sick days would be taken away.