FrogReaver
The most respectful and polite poster ever
It's not about precise phrasing though. If I'm not going to tell you what your character thinks, then it's only consistent in my view for me to also not assume or establish what your character is doing. To that end it's on the player to describe a goal and approach that I can adjudicate.
I am saying that when I and many other players say X we actually mean Y. You are saying no matter what is meant by X you require a player to say Y. It seems to me like if the meaning in both situations is the same then it is coming down to being about how something is being said.
The point is that even when I as a player say "DM tell me if I think he is lying" I don't mean for you to literally do that. It's shorthand for me that means the same thing as "dm I am going to watch him and his reactions to see if I can determine if he is lying".
Should you have to make such assumptions about the PC's actions as the DM? I think you can't avoid that completely. I think that as long as the player is generally accepting of the assumptions you make on behalf of his way of phrasing actions then the game works just fine. If the players keep challenging whatever assumptions you are drawing from their shorthand phrases then it's probably time to require them to be more specific.