[MathsOX]

Princeton doesn't do transfers, Harvard/Yale have 1-2% transfer acceptance rates, etc.

When transfers are admitted every year to my school (usually just 5-10) there's a writeup in the school paper about them. Without fail they all a) were accepted here, but chose to go to a similar/competing school like Princeton and b) are exceptionally accomplished at a young age.

[scarmig]

This shouldn't be taken as the typical situation at all, but I know of a guy who transferred from a CSU to Stanford (and went on to get his JD from a top law school). So it does happen.

In general, it might not quite be the case that it's (particularly) hard to transfer from a state school to an elite one. It's just the universe of people going to more democratic schools are distinct from those going to elite schools; in other words, if you took a random sampling of students who have no issues getting into top schools straight from high school and put them in community colleges for two years, they would have no issue transferring to a top school afterwards.

[MathsOX]

Stanford has a transfer acceptance rate of 2%, so good for him. As for your second point, that's likely true, but it'll still be much more difficult for them to transfer than to get in straight out of High School (and impossible at schools like Princeton).

Every transfer at Harvard I know of was admitted to Harvard, but just decided to go elsewhere before deciding Harvard was the right choice.