I have read I should encode my ampersands as &
in HTML.
However numerous code samples from respected companies somehow forget
Is there any real benefit from not escaping ampersand in links?
It saves a few keystrokes.
Is this related to browser quirks?
No
Is this just a mistake in documentation?
Yes
Is there a reason API documentation by respectable companies often violates this rule?
Ignorance and/or laziness. Browsers perform error recovery so they either don't notice the errors or they don't care. The documentation probably isn't written by their best experts.