The above is both correct and incorrect.
It is true that prompts like those shown above are presented to the model as instructions on how to use the browsing tool.
However, the issue is that ChatGPT doesn’t always browse according to those prompts.
I’m not sure if this is due to the difference between the prompts presented to the ChatGPT model and the language the user is using.
Considering that most people use ChatGPT without knowing what prompts are presented to the model about how to use the browsing tools, I don’t think you answered OP’s question.