Great summary. Number 1 especially drives me mad, as so many people still firmly believe it and are depriving themselves.

I would like to qualify #2 a bit though. While what you say is true, some people are unable to properly digest carbs, and so need to be careful what kind, For myself, I do fine on a few small serves of fruit and some low to medium carb vegetables each day. But I can't regularly eat high carb veges, grains or legumes without putting on weight. Sad but true.