This doesn't seem so hard to understand. In the limit, you can see that an employer can't keep paying someone who is sick all the time and who is not working. The employer is providing a guideline about the amount of sick time it can accommodate before the situation becomes untenable.
So to answer my direct question... That means that the employee should come into work and get everyone else sick? Maybe I'm dumb, but I'm still not understanding how that benefits the employer. "Tenable" or not, it's the reality of the situation, and what you're describing sounds more like saying that the employment of that person isn't viable due to their health issues. Which has nothing to do with pretending that the employee isn't sick.
It means that:
1. The employee doesn't come to work sick because that is not considerate.
2. The employer provides a reasonable amount of sick time which is compatible with her staying in business.
3. The employee uses the sick time when she is sick.
4. When the employee is sick for longer than she has sick time, she can ask the employer for some accommodation which the employer can grant at her discretion.
This may seem like a description of some quaint and fantastical world in which people are considerate of their coworkers and they don't dishonestly use sick time for vacation, but there's your answer.
Okay, that kind of makes sense: formal sick days are the amount of times you can call in sick no questions asked, above which you need to communicate with your employer.
Thanks for the explanation, though I have to say I could've done without the whole "being a dick" facet of your comments.