> is the author advising us to stop the long-running advice of "speak precisely" with "say anything, even if you are not sure' with the only caveat being to let people know when you aren't certain of something?

You got it all wrong. The key point is that by adopting a conversation style where you cease to impose your beliefs as unquestionable facts and start to leave the door open for others to provide their observations and insight, you start to get observations and insights from others.

It's as simple as that.

And by the way, your personal opinion is not precision or an expression of a fact. Your personal opinion is just the conclusion you've made based on the information and experience you had up to that point. If you cease to be defensive about your opinions when sharing them with others, others will follow suit.