The gist is right, perhaps a little civility would make the message more palatable....honey/vinegar. I also post a link to our state's driver's manual, which has an entire chapter on sharing the road with cyclists, including the part where we aren't supposed to ride on sidewalks, with a blurb for those too lazy to click.
People simply don't get it. They don't have the experience of riding amongst themselves so they don't understand. Like you said, they get behind the wheel and it's all about them them them them. Then there are people like my dad too. He was driving up a hill with no shoulder, coming up to a cyclist and he complained that it was too dangerous to pass because you couldn't see oncoming traffic due to the hill. I suggested he wait until it was safe. You could see the light bulb brighten, it just didn't occur to him that you could wait. It was only for several seconds and then we carefully passed. This is one of the, no, the gentlest guy I know who does think of the others on the road and is careful but hadn't realized.
Since we can't get them to bike a bunch of miles in our shoes we have to rely on education, sweet and gentle and lots of it. It shouldn't be us/them, we aren't sides, we're people. On the same note, if any of y'all are the sort that bike with a me me me attitude (saw a lot of that at the last group ride), zipping through stops, taking up lanes unnecessarily, etc, well.....
I used to have an open mind but my brains kept falling out.