Yes, you need a perfect run to take first place.
That makes champion quite a bit harder then I think it should be. If they make the weakest NPC a little stronger, it'll reduce the gap while making tournament play overall a little harder. If they make the strongest NPC a little weaker, it'll make tournaments overall a little easier. Either would be fine, but right now the lead is quite ridiculous.

I should also say that in my 15 tournament championships, I only got one platinum pack ever. Most championship gave 3 or 2 packs. I'm not sure if that's something that would change if I played better, or if it's purely random chance.