Scott,
You seem to be assuming driving, right?
By train, leaving Basel at 6:01 would get you to Zermatt at 9:14, i.e. 3:13, not too far from the three hours suggested.
Not being a skier I have no idea how convenient it is to carry skis, boots etc in the train, but the existence of the Snow'n'Rail program strongly implies that it can be done
I obviously did not test the (many) other times in the list, but they may well be possible.
Hmm .. I obviously should have tested a few others.
Train Basel Andermatt is about three hours, not 1.5. Basel Champex-Lac is close to five hours. Hence I assume that Carlodons was referring to driving times, and was, as Scott suggested, optimistic.