The problem is there's a finite amount of rings in each stage, and it certainly won't be long until more than one person gets all the rings in say, GFZ1. If both me and my friend can both end a stage with all 174 rings, but I take one minute and he takes 50 seconds, then he should quite obviously get first place on the leaderboard, not me.No, I think it's just the overall number of rings you carry to the end sign, regardless of time.
(Score is technically also finite and "solvable", but being that the max score involves "bouncing on as many enemies in a row as the stage geography allows" ties will be much more uncommon, so time isn't as important here.)