Yet companies act in exactly that way towards their employees. Late too many times? Ultimatum is issued where you get fired if it happens again. Too many sick days? Same result. Underperforming? Yup, you guessed it. Your employers are not your friends - do what you have to to make your life easier. IMO, ofcourse.
A good employer will talk to you and try and work things out before giving you an ultimatum. You lose little, and can make things a lot easier, by doing the same.