At what point is water considered “at a boil?”

No. The amount of salt you would have to add to water to make an appreciable difference is enormous.

Salt is added to water for various reasons: to season whatever is being cooked in it; to maintain colour; to maintain structural integrity.

Adding a starchy substance such as rice or noodles to boiling water increases the surface tension of the water. When it's just plain water boiling the surface tension of the water can't hold back the force of the steam rising and the bubbles burst. Starches increase this surface tension making the bubbles more elastic/pliable (essentially creating a foam), thus requiring more force for them to burst. This makes the bubbles last longer which allows them to build up and eventually boil over.

It's more likely to occur with anything starchy like rice and pasta.

A lower temperature should help to control a boil over as it will allow the water to cool somewhat and slow the boil.

I'd assume that, from your quoted text, that if you use less water you're still imparting the same amount of starch making a thicker solution. More water would dilute this and bring it closer to normal water. In my own experience, small amounts of water allow lots of bubbles to form but nothing really boils over, it just splatters a bit. But reducing temperature and tilting the lid to let some air in has helped me in the past.