I worked in a hospital for 8 1/2 years and we were on a similar system. Lets say that you called in 3 days in a row but you went to the doctors office and got an excuse then the first day would be an unexcused call in and the following two days would be excused. If I remember correctly we were allowed to call in 3 times in a 6 month period. On number 4 you got written up. I can remember two instances that I had no control over that I HAD to call in and it went on my record. I didn't care...it went off my record after 6 months...I wouldn't worry about it too much.
The bad part about taking sick time is that you only received 60% of your pay...which makes a lot of people think twice about calling in. If you are a full time employee you receive 40 hours of personal time that you can use for any days off that you have or want. Everyone accrues sick time and vacation time. Sick time can only be used if you need to schedule a doctors appointment, a hospital stay, or a call in. Vacation time could only be used if it was approved in advance.