leaving 163 crucified children as mile markers.

There's no evidence unless you'd like to quote. It's not an implication it's a characters unfounded assumption.

Who else could make a decision that speaks for the leaders of the city like that?

It doesn't speak for the leaders of the city unless you've made that assumption without evidence. Literally anyone could do that unless you have evidence of how they're governed.

How do we not know this? We know the slavers are people with agency, right? If they're people with agency they could stop someone for sending a incredibly public message that they don't agree with. They also could make it clear that they didn't agree with the message. None of that happened.

Because Dany has not made any effort to find out. Very simple, I said it before. That's how we don't know if your assumption without evidence is true. If they're people with rules, they may not be able to stop another slaver acting in a legal manner. Again, if you'd like to quote your evidence about the governance.

Dany clearly assumes the leaders of the city would be the ones that were guilty. That's why she asked for it's leaders.

She did so without any evidence of any kind which means her assumption isn't evidence either. She saw them on her way to Meereen and assumed the leaders did it without any evidence.

What reason would they have to not throw the actual culprits under the bus if that's what what they were worried about? Might as well try, right?

Again, quite simple. When your conqueror tells you to give up 163 of the most powerful to keep her from killing all of you, you don't sit there and try to negotiate. Then you might not be spared.