Being paid cash but still getting taxes taken out...

If you are being paid cash, or "under the table" as some people like to call it, should the person paying you still be allowed to take out what would have been the taxes taken out if they paid you on the books? I don't know what made me think of it, probably weird pregnancy brain, but years ago I went back to work part time at an old daycare center I worked at while I was waiting for my teaching job to come about. They actually reached out to me and told me they'd pay me cash for whatever hours I could work...then when the time came to pay me the guy, owner, paid me the cash but took out whatever taxes would have been taken out had he put me back on the books...I was young so didn't say anything but last night I was like WTF he shouldn't have done that I was on the books and it was cash!