"Listen, Chimchar, don't worry about Blaze. We don't need Blaze, we won the Tag Battle without it, right? You got lots of strong moves. Look, Chimchar, you gotta believe in yourself, and stay strong for the both of us."
The original dialogue goes roughly like this:
"Listen, Chimchar, don't worry about Blaze. You didn't use Blaze during the Tag Battle, and we won that, didn't we? You have lots of strong points. Right now, you have to believe in that and believe in yourself. Let's go all out!"
It's slightly different, but the connotations are mostly the same, and you didn't really remember it correctly either - he never says anything about Paul, the point he's making is just that Chimchar is capable of fighting even without Blaze, so it shouldn't let the fact that it can't use it keep it back like that. The episode is oriented around the fact that Chimchar feels weak and worthless because it's unable to use Blaze, and Ash telling it that's not the case, it has lots of other qualities to make up for it. So... there's no plothole or inconsistency in either version.
(unless you're thinking of a different line, I just skimmed)