@BaDumSsh
Absolutely the parents' responsibility and one hopes the parent will have the greatest interest in keeping their child safe.
However (and this may be age on my part or being a teacher) I also expect community to be engaged in keeping every citizen safe, from offering to carry an tottering old lady's shopping even if it takes me a little out of the way to being able to expect someone to say and having myself the responsibility to say to the ten year old throwing snowballs at traffic from the suspect branches of a rotting tree..." get down from that tree now - those branches will not hold your weight and you could cause an accident throughing snowballs at a car", or similar.
I do not expect another mother to scream at me "it's my child, don't you dare speak to him. It's up to me if he wants to hurt himself or not", when I say to her darling playing with the heavily sprung doors in a changing room, "watch your hands/face, sweetie, that door is going to hurt you."
Nor do I really expect in a family friendly social gathering (Church "bring your children too" party), in a closed room, for a adult faced with a two and a half year old approaching at a clumsy toddler run closed door, to open the safety-catch door FOR NO ONE OTHER THAN THE CHILD and let them out to a straight run (the outer doors were open) to the car park and the dual carriage way beyond that.. (luckily I was watching as was another parent, quicker than I, who caught my son).
I appreciate the middle-aged man who did this was not a dad and was trying to be courteous (no common sense).
So yes, the parent has the responsibility ultimately but so do we all towards every other person in our community.