Flew in and out of JAC for several years in the left seat of AA 757's as a line CKA. The south end of the runway could be slick as snot with any thaw and refreeze of water thruout winter days whenever the sun happened to break thru and cause a thawing of any ice on the first 1,000 or 1500 feet of the short runway. AA landing procedures at JAC for the 757 are 30 degrees flaps (full), wing spoilers armed and auto-brakes set at "4" or MAX, either one, at pilot discretion. In the mountain airports or anywhere on shorter or slippery runways, AA trains pilots to plan for and fly the aircraft to a firm touchdown with throttles at idle simultaneously with touchdown and immediately holding light pressure against the thrust reverser interlock detents while smoothly but quickly flying the nose gear onto the runway whereupon the reversers unlock and full reverse thrust is called for during at least the iniital rollout. Of course proper functioning of auto-brakes, spoilers and reversers are briefed to be watched for diligently.
The Captain apparently informed his passengers that the brakes were malfunctioning, who knows to what extent, but as mentioned, those big fans on the RR RB211 are very powerful stoppers, just not as good as wheel brakes once all the weight is on the wheels. Note (yes the RB211's AA uses on it's fleet are of the same family powering certain A380's of recent fame)
Many variables involved, of course, but generally for the shorter city pairs to JAC, like ORD-JAC and DFW-JAC dispatch would have us ferry fuel to save some $$$ since fuel in the mountain airports is astonishingly expensive. That would put aircraft in relatively heavy weights for arrival. My personal operating mode was to refuse ferry fuel when the runways were going to be slippery. I had another quirk that maintenance took about 4 months to adjust itself to. I demanded nearly new or new tread on my tires for mountain flying year round. The FO's loved me on those sometime cold winter days as I did the preflights, going to the tires first. After a few flights delayed for my demanded tire changes, the maintenance department was informed by dispatch whenever I was scheduled to fly to check the tires ASAP on mountain flights I was scheduled for.
At first, when a tire change was called for, a mechanic would check the tires and note the tread was usually within AA Maint/Opspecs. I would always inform them that, yes it was so; but the tires were not up to MY opspecs, for short, slippery runways and usually full of pax and ski stuff. I told my trainees on mountain airport checkouts that was a useful technique (Captains' opspecs) to keep in there repertoire for later usage.
In recent years, don't know if they still are, but suspect it is so...... AA trains pilots to "hit" cities with computer based video flight checkouts. I think Tegucigalpa might be the only city they still actually physically check out a pilot to fly to and perhaps the V-Nav approach to Eagle.