Do Stats rise from Levels alone?

Alright, I was boosting the chars in the Dinosaur Forest, and while I was boosting Terra's Mgc. Pwr, she seemed to gain THREE Magic Points from a Magic+2 Esper (Tritoch).
I went "what the hell?", because I thought they never raised from just leveling up.
However, they must do, because I think one of my chars got 128 in Vigor AND Mgc. Pwr once, and that seems impossible from just boosting with Espers.

Your characters stats rise depending on what Espers you equip on your characters. your characters stats can still rise by leveling up, but it's best to equip espers on characters because some espers have leveling up bonuses