unreasonable sick leave policy?

A reader writes:

I work for a well-known hospital in New York City. The company administers an employee satisfaction survey every year, and for the past few years there had been an increasingly negative response to the policies concerning sick leave. We accrue 90 hours of sick time a year (twelve 7.5 hour days). The original policy tied the number of days that you were out sick to 20% of your performance evaluation which, in turn, directly impacted your raise. This year, the HR department revised the policy, stating that it was no longer tied to your performance evaluation. However, any absences over 4 days within a 12 month period now result in disciplinary action. Here is the breakdown:

Over 4 days - counseling
Over 6 days - verbal warning
Over 8 days - written warning
Over 10 days - final warning
Over 12 days - termination

I assure you that I am not exaggerating in the least. How is it that the hospital can give us 90 hours of sick leave a year and then fire someone if they use it? There is no standing requirement that employees turn in a doctor's note unless they are out more than three days consecutively. I might add that the nature of my work is very stressful in that we deal with a high volume of very sick patients. Is this even legal?

It's legal but parts of it are not particularly wise or fair. Basically, the hospital is saying that if you use more than the number of sick days provided, it's grounds for termination. That's not that unusual; many employers draw a line in the sand about how much absenteeism is simply too much.

But what stands out to me about this policy is that there are various disciplinary measures well before an employee reaches that point. Why give you 12 sick days if you're going to start getting warned after using only four of them? It's silly and sends a message that you don't really have the 12 sick days they claim you have.

(I am assuming, by the way, that the employer makes the legally-required exceptions for FMLA, etc.)