This question is about getting out of US by land.

Has anyone with a valid destination visa/visafree ever been refused land entry into Canada/Mexico?

It appears that border guards can refuse people entry at the border for whatever discretionary/discriminatory reason. In that case, what happens next? Do you simply get returned to US? But you no longer have a valid visa/esta nor can you apply for one.

Also, physically speaking (take for example, leaving a sanctuary state by Amtrak into another country) do you exit US customs before entering the next country's? Or are they one-and-the-same with no physical "limbo" space?