Law professor explains how United blew it.
Neither of the two rules cited by United, Rule 21 and Rule 25, apply to the doctor's removal.
http://lawnewz.com/high-profile/united-cites-wrong-rule-for-illegally-de-boarding-passenger/
United’s Rule 25, as its title clearly implies, applies only to denied boarding. Thus, it uses the word “denied boarding,” and variants such as “deny boarding,” but says nothing about requiring passengers who have already boarded to give up their seats.
Indeed, it states in part, using the word “boarding” twice, that: “other passengers may be denied boarding involuntarily in accordance with UA’s boarding priority.
Clearly, a “boarding priority” does not include or imply an involuntary removal or refusal of transport. Moreover, under well accepted contract law, any ambiguous term in a contract must be construed against – and in the way least favorable to – the party which drafted it.
SNIP
Rule 21 . . . which unlike the denied boarding rule does provide for removal “from the aircraft at any point,” lists some two dozen justifications including: unruly behavior, intoxication, inability to fit into one seat, medical problems or concerns, etc. But nowhere in the list of some two dozen reasons is there anything about over booking, the need to free up seats, the need for seats to accommodate crew members to be used on a different flight etc.
SNIP
Finally, it appears that United is seeking to blame the passenger, claiming that when asked to give up his seat, he acted belligerently – and citing a rule which requires that passengers obey the orders of the flight crew. But, such a requirement applies only to orders which are lawful.
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I charge the lowest interest rates allowed by law. 
The airline industry should be ashamed... And to think the Republicans are currently advocating privatizing and turning over the Air Traffic Control responsibilities to the airlines. 
