The car question is a metaphor for ANY silly question asked for a Gadol. I dont know if Rav Chaim was asked if someone should by a Honda Accord or a Toyota Camry (I have heard people asking a Shailia which car to buy) . It seems that point was lost and people took it literaly. I can tell you I have heard really silly questions that were easily answerable that people got “Daas Torah” on nonsense that any normal human being could have answered.
As far as Rav Moshe and the Simple Shaila question, yes Ive heard that story, but I have also heard stories where people would ask annoying Shailos and then got the Shammai treatment