Many years ago I looked up the details on what a SARSAT beacon transmits to the satellites.

The key thing is that there's only so much space in the packet transmitted, and some of the least significant bits/digits of the location are not sent.

My memory is not clear, but I think the digits transmitted amount to a minimum 300' circle. It may be larger, but the point is that it doesn't matter how precisely the beacon's GPS can pinpoint the location: only a limited number of digits can be sent.

In the best conditions a good GPS can get to < 30' precision, but these were not the best conditions. Her GPS may not have been able to calculate a fix even as small as SARSAT's capabilities based on where the beacon was and how the atmosphere was distorting the signals in the storm. And with the wind it's not hard to imagine the beacon being promptly covered by ice, dirt & debris even if the beacon was in a good spot for listening to GPS satellites.

Finally, beacon GPS may not have even come into play. The Fish & Game guy said the error circle was about a mile. That used to be the precision for locating the beacon by "triangulation" from the SARSAT satellites when no GPS data was available. If this capability still exists it's not hard to imagine storm-driven radio distortions causing a satellite fix to wander a lot.

Mount Washington weather is notorious even to non-hikers. A weather radio would have been a good idea.

PS. A GPS receiver generally uses a temperature-compensated oscillator in the timing measurement. It may have been too cold for the GPS receiver to calculate a position!