I don't know what the dub did, but I'm pretty sure they were only referred to as full battles. And unless you knew about full battles, it doesn't automatically equate to it being 6 on 6, we know that a full battle is a 6 on 6, but because we were told that's what it meant.
But if someone didn't know jack about Pokemon, like say your hypothetical cousin in a country that has no internet, or knowledge of Pokemon, it's unlikely he'll be able to discern that full battles = 6 on 6 battles.
Now Cameron obviously knows something about Pokemon, he's a trainer with conveniently powerful Pokemon, and you'd think he would know what a full battle actually is. But it could've easily been something that was never came up, similar to the situation, where you're trying to find someone and you coincidentally keep missing them.
Or it could be as simple as he was lied to by his parents, or something, who only wanted him to carry 5 Pokemon instead of 6, although his reaction was clearly more because of the former than the latter.
I mean looking at Cameron and who he is, I could see why his parents were to hypothetically lie to him, I mean could Cameron even take care of 6 Pokemon once, or is he going to forget, and then when he does remember, he sends out his Pokemon only to find a pile of bones.
So in the end, it's the trainers' parents that never taught their children proper lessons.
When your senpai notices you at last and you're all like: