Hi Apskip, in my above analysis I only described the journey made by LaKisha/Jennifer, who were seen on a train that was going from Chur to Zurich. As you said, there are direct trains from Buchs to Zurich, so the sisters, if they had started their journey at Buchs, would not be on the train they were on. They must have started riding the train at Sargans.
IR 1776 from Sargans to Zurich, 1239-1348 (LaKisha/Jennifer seen on this train)
IC 826 from Zurich to Visp, 1402-1602
R 249 from Visp to Zermatt, 1625-1734
If they had started at Buchs (false theoretical scenarios):
RJ 364 from Buchs to Zurich, 1212-1320
IC 826 from Zurich to Visp, 1402-1602...
R 7955 from Buchs to Sargans, 1310-1325
IC 576 from Sargans to Zurich, 1328-1423
IC 828 from Zurich to Visp, 1502-1702...
It is unsure whether other teams would start from Sargans or Buchs, but if TPTB likes to keep teams close together they may have arranged for everyone to start at Sargans, either by explicit instruction, or by having the moped drop-off be at Sargans.