I generally agree with your assessment, but if you don’t think she misspoke, you’re going to have to explain her prefacing the statement with the word “while.” Grammatically, that sets up a contrasting statement. If you don’t believe me, ask an English teacher.
Here’s the transcription of her statement:
“I’ve made it very clear that I work with the police and instructed them to do everything that they could to make sure that the protesters were able to exercise their right to free speech. It’s a very delicate balancing act, because, while we tried to make sure that they were protected from the cars and the other things that were going on, we also gave those who wished to destroy space to do that as well. And we worked very hard to keep that balance and to put ourselves in the best position to deescalate, and that’s what you saw.”
You sort of choose to ignore the “also”, an inclusive addition.
bye bye