I think that you did the right thing. It does happen that a child is disciplined for something he did not do or which turns out to be different than what the teacher or helper saw. It also happens that a child is not caught doing something against the rules and is not disciplined. It all works out. What is important for your son to learn is that the person in charge of him is responsible to call them as he sees them and even tho the one in charge made a mistake he is to be respected.
When what happens is serious and obviously in error, yes, you do need to stand up for your son. This is a minor situation about which you should not be concerned about. If you had not seemed unsure your son would have long ago forgot about it. You should be concerned if a pattern develops in which your son is frequently disciplined for actions that seem unlike him. Then you need to ask lots of questions.
If the school staff investigated every situation like this they would have no time for the normal day to day interaction with children. The school would be more focused on wrong doing and discipline then on teaching children how to behave and providing a positive experience for the children. Second guessing a minor decision such as this is counter productive.
I have been doing lunch playground duty once/week for 5 years now. From time to time I blow my whistle to stop some behavior. Sometimes the child wants to convince me that they did nothing wrong. I have more of a tendency to add additional discipline, such as a time out, when they argue with me because of the arguing and not the reason I blew my whistle. I say to them that I'm only concerned that the action stops and not who did what. Can they go back to playing "nicely." I insert whatever I am concerned about.
What I've described about my experience as a playground volunteer concerns children who are older and more mature but I suggest that the seeds for this kind of behavior is planted when the child is young and the parents focus on guilt instead of respect for the process. There is frequently no way to know what actually happened. At the same time there has to be a consequence, especially during the early years, so that the child learns about good behavior and consequences.
The girl fell. Your son is 4. He may have reached out to her and doesn't realize that his action contributed to her falling. He may not have actually slapped her but he may have been angry or irritated with her and it showed in his face and posture. The playground supervisor did the best he could based on his skill level.
Your child will always be around people who are not especially skilled. The day care cannot afford to hire a professional for playground duty. He is learning right along with your son. If he makes errors repeatedly the teacher will recognize that and if not you can bring it to her attention. In the mean time give the young man the benefit of the doubt.
You have to trust your provider. I suggest that you could still talk with the teacher about what happened but I urge you to keep an open mind and not push for a resolution concerning the time out. Ask because you want to understand the system as well as know more about this young man so that you'll feel more comfortable.
Young boy really tells me nothing about this person's age. The way that you stated young boy and put teacher in quotes causes me to wonder if you are having difficulty with this because of his age. If he's truly young, say 14-15 or less, then I might question what he did. But if he's older than that he may have good skills for managing preschool age children.
My granddaughter has been in the after school YMCA child care program for 5 years. The best caretakers have been young. They do have to be at least 18 and I think most have been 19-22. This years site director seems to be perhaps as old as 24. I've been on field trips with them and seen them in action. I also volunteer at the site and just hang around when I pick up my granddaughter and know that I can trust them. A couple of times I wasn't sure what was actually going on and I asked the worker. I've been confident in their ability to supervise her and the other children except during one year when the workers were changing every few weeks.
If you're not sure about your son's care, find a way to spend some time observing the workers at work.