Is AUTHOR wrong in the post ? POST : I know this already sounds bad but hear me out.

At our local mall, we have a play place I like to take my 2 year old son to so he can let his energy out. The play area is an open area with large soft decorations the kids can climb on. It's enclosed in a square but there is no door or gate to prevent kids from leaving (and I suspect so parents don't just drop their kids in and walk away). There are benches within the play area where the majority of the parents sit. Most people will watch their kids play but a lot are usually distracted by their phone. 

My son is a runner and will tear out of the play area in a flash so I always stand at the entrance/exit because I have to watch him like a hawk and will redirect him if he's trying to escape. 

More than a few times I've stopped children to leave because people aren't paying attention but today this one parent in particular would *not* pay attention. I stopped his (around 18 month) child twice but he didn't acknowledge me or say something like "Whoops! Thanks, I was distracted for a second!" This guy wouldn't get off of his phone (texting or internet browsing, I'm not sure) so his kid kept wandering away. After the third time he didn't notice her leaving- I didn't stop her but waved to get his attention so he would. Again, he said nothing. The FOURTH time this happened, I did nothing (I'm not a monster wanting a kid to get abducted, I was still watching her out of the corner of my eye but I was waiting to see how long it would take him to notice). 

About two minutes later, he saw her wandering behind the benches, ran out, picked her up in a huff and very loudly yelled at me for not stopping her because I'm the one at the exit. Then all the other parents were nodding and throwing *me* dirty looks. I took my son and left after that.

AITA here? Does standing near the exit automatically put me on unspoken guard duty? 