Of course there is a distinction. If you are ticketed DEN-LAX-MEL, you would be entitled to a paid room / voucher if you reside anywhere except LA. If you reside in LA and are ticketed DEN-LAX-MEL, you are not. If you reside anywhere in the world, but are ticketed LAX-MEL, you are not.
As to crew time out, all it takes is a 2-hour WX / ATC issue at LAX or enroute and the crew times out and UA washes its hands. Once the aircraft is airborne, it's all fine.
All three carriers are quite adept at washing their hands for other than their top-tier elites and the top tier elites are taken care of as a matter of customer service having nothing to do with contract.