I think pretending the President sits on their hands all day waiting for Congress to decide its own business with absolutely no input or badgering from the President is a soft lie, and lets the President off the hook for not corralling their party into line and/or for promising to do things they knew they would not expend political capital to get done.
Yes Presidents obviously try to have it both ways; they talk about their agenda and the things they want to do while running, but when they break their promises or fall short they defer to giving everyone a civics lecture about the seperation of powers.
Yet contrast it when they pass stuff.
We still call it Bidens Infrastructure Bill
Or Trumps Tax bill
Or Obamacare
Etc etc