The principals of rotational/angular momentum and inertia.

Same reason you get more stable with speed (up to speed shimmys from an inbalance. There is a difference between linear physics and rotational. If our friend is an astronaut, they would have studied this in a pre-requisite for getting into the program, or at least in high-school physics. Earth's gravity plays no role.

This is the same principal that lets a top spin on a small point and not fall over. It is not magic, or defying gravity. Its rotational force and momentum are just stronger than the force of gravity. When, do to friction, the angular momentum is not stronger, then it falls.

The wheel has angular momentum and it is based on an axis. Moving it upright changes that axis, and thus it is a "new set" of momentum and intertia, just in rotational way. Same story of when you make a turn, you are not going as fast, but still cary some speed.

Though small turns aren't too noticable, this is why a lot of turns takes more energy than just the extra distance traveled.

This is why wheel weight at the rim is more important to racers than the weight of their seat post.

I was even told by a physicist that angular momentum is what allows a nicely thrown football to travel farther than is should (based on linear physics alone). To that, I don't know...