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