Sadly, there are so many ways around that it isn't even funny. Let me make it clear...most people do not abuse the system. The ones that do not only ruin it for everyone else but they also, by association, cast a shadow of doubt toward those with legitimate reasons. It is so easy to get a Doctor to verify something for you. Litigation has made Doctors decide that agreeing with the patient is less likely to open them up to lawsuits then if they deny it and then something is really wrong. So tell them you have a problem and they will, if unable to absolutely dispel it, go along with it.
You are correct. It may seem easy to fill that position but it isn't easy. If it were one wouldn't have much job security would one. The PTO system is probably the best in this age. If you are willing to take time away from your actual vacations, then use all the time up for sick time you want. Most companies will not run benefit time in the red. Use it up and that will be it. The company can refuse to give you time off for anything after that and if you take it anyway, without pay, you can be fired, which is probably the way one would be headed anyway with enough absenteeism.
I remember one of the most annoying things was when someone took FMLA leave for 6 months and as soon as they came back would take two week or more vacation. This put unbelievable stress on the workers that had to fill in for them.