I'm from UA, but I guess that since your original post was July, you may have found the answer by now !

To be honest, it depends from station to station.
Internationally, we work differently to domestically.

We still apply to other airlines for interline travel as well as utilising the self ticketing agreements. Generally, applying for interline travel on another carrier is
restricted to business travel, but on occasion, also for pleasure travel.
In London, we have a list which has been compiled from the monthly interline lunches that are held where the person responsible for ' Industry travel ' from each carrier usually attends. It's networking !

Our policy is, if another carrier charges us, we charge them !

However, I appreciate your question is directed towards a domestic market and to be honest, your best bet is to walk up to the ticket desk and purchase a ticket, if they charge you the YQ ( Fuel Surcharge ), challenge it !
If they are hell bent, tell them to void the ticket.

I am anti fuel surcharges. As employees, we pay more than enough government taxes on tickets, which far exceed the fare we actually pay.
Over the years, the amount of tax we pay increases, fuel surchage internationally stands at £181 roundtrip, so almost $400 - it's no joke !