Ok, the first point I must've misread (or they edited, since I thought I directly copied what they said). Either way their first sentence is now correct.

The 2nd point is only true if you add the caveat "it takes more force to move a mass the same amount of distance in the same amount of time". You're absolutely right that this is going to come down to the work done over the distance travelled, but the OP didn't mention work at all.

Another way you can think about it is if I drop a bowling ball from 1m high on the moon or on Earth, in both cases it will drop to the floor. The moon has lower gravity and hence a lower force will be applied to the bowling ball on the moon. And yet the bowling ball will move the same distance in both cases. It will just take longer.