yesterday I hurt myself at work and i had 3h left to finish and my
manager saw how much pain i was, could barely walk, said i should go
The question is, does your getting hurt at work mean something other than just an impact on your Bradford score? If you are hurt enough to not do your job, then maybe you were hurt enough to go to a doctor. That may mean that the company has some responsibility for any impact on your pay or medical costs.
Yes every absence for "medical" reasons is an absence that is counted. I worked for a company in the United States back in the 1980's that used a similar calculation. Vacation didn't count against you. But sick leave did. One reason is that vacation days were planned in advance, while some or all of sick leave wasn't.
Also incidents had to be counted carefully. If you fell at home, then went to the doctor, then a few days later after the swelling went down had surgery, but then had 10 times you had to miss time for physical therapy during your recovery; That was one incident.
The Bradford score is not something to be used in a vacuum. Trying to get employees to avoid a lot of little absences is the point of the Bradford score. But forcing them to never go home when sick or injured can be the result.
When I worked for that company It just meant that everybody found a way to manipulate it, and management used it to reduce the performance review score of those they wanted to not give a big raise to.