Maybe referring to the Elite Four second Round? Which isn't exactly the case. Or maybe the Trainer Tower...
As for the idea... I like it. Rival Battles are some of the best, because they're not retarded Monotype users. Making it even with the level of your Pokémon would be awfully superb as well and add this bit of challenge the franchise badly needs in regards of the main story...
Not to mention it'd punish turds that apply the no-skill playthrough of "Train-Your-Starter-'Till-The-End". People would be obliged to train their Pokémon as evenly as possible, or be owned in the process. Which is good in my eyes.
And well... maybe only the Rival's main Pokémon (Namely, the Starter he/she went with.) should be the one on par with the Level of you highest Pokémon, while the others would be a few levels lower, setting a floor of 7 levels below, and raising depending on the Pokémon. Just an example.
Even then, good idea. I'm all for anything that adds at the very least an ounce of challenge in the main quest...