I've been using wheelchairs in and out of LAX for years with no problems. Alaska Air has a good program. With most airlines you must make the reservation for a wheelchair ahead of time, with the airline, not the airport.
I can walk, some, but with a bad heart, not too far, and with a bad knee not up or down stairs at all. Agent is just being difficult. Contact Alaska and ask if they can meet her at the arrival gate. That will zip her thru customs and everything. (Customs is the worst part of being not very mobile because the standing with no support is worse than walking.)
Using a neck wallet with passport, boarding pass, itinerary, a credit card, and some $1.00 bills or equivalents for tips is very useful if you are in a wheelchair and can't easily access your bags because you'll need to show passport and boarding pass several times more than walking people do.