I'm absolutely right

I wonder if this is a tactic that LLM providers use to coerce the model into doing something.

Gemini will often start responses that use the canvas tool with "Of course", which would force the model into going down a line of tokens that end up with attempting to fulfill the user's request. It happens often enough that it seems like it's not being generated by the model, but instead inserted by the backend. Maybe "you're absolutely right" is used the same way?

It is a tactic. OpenAI is changing the tone of ChatGPT if you use casual language, for example. Sometimes even the dialect. They try to be sympathetic and supportive, even when they should not.

They fight for the user attention and keeping them on their platform, just like social media platforms. Correctness is secondary, user satisfaction is primary.