By "school" I assume that you mean elementary school, not preschool or daycare.
If that is what you mean, then yes--what you experienced is par for the course. IME the only thing you really get notified about is if something is serious enough for the child to be taken to the nurse--and even then if it's just something like a scrape or minor cut not even then. It can be a shock from daycare/preschool, where because of insurance and legal liability you will receive an incident report for every little thing, or even if they took a tumble with NO bruise, ect.
I often heard about little incidents from my kids' teachers, but most of the time that was because (in the case of DD) I picked her up and hung out for a bit every day or had pretty close contact with the teacher.
Generally, it's not the teacher who is supervising on the playground though. So if your kid gets pinched on the swing, gets a broken blister from the monkey bars, or a scrape or other bruise it's not like the teacher is going to know either unless the child tells them or they need the nurse.
What you describe for an elementary school, IMO, is normal. If it happened at a preschool or daycare, I would be concerned.