[Come on Damian, you just mentioned how Alfred had saved you when you were younger, and that there had been no other adults, and he knew Damian had started woking with Bruce when he was still a kid. Plus Damian had been super avoidant about mentioning himself-- maybe he couldn't be absolutely certain, but he could assume with all the conviction of a child convinced he was right based on even less evidence.

(It seemed pretty obvious to him right now, and yet it didn't even cross his mind that if Damian was the subject of the story, that mean he would be Ra's al Ghul's grandson. Hopefully he'd remember when he was able to move around, and think to take another look at the files in the computer. Before freaking out about it.)]

But Batman helped save him. If Ra's wanted to do that, then I think he was kind of already an enemy of the League anyway. 'n' if he wanted to be Batman's partner, that means Bruce would be able to teach him to defend himself from ninjas too if Ra's wanted to try and steal his body again.

[Maybe Dick was a bit biased and didn't quite realize how dangerous and stupid it was to volunteer to be Batman's partner.]

Letting him stay with Batman would be the best way to keep him safe from the League. If I were her I'd be scared of what the League would do next and get all the help I could get.