Actually no. Because you do need a whole lot of evidence to prove such a claim. Extraordinary claims require extraordinary evidence. The burden of proof is on the positive claim. It appears to me that you have some warped sense of understanding about how things are supposed to work. I have already gone over "space-time/fabric of reality" argument in my earlier comment. Repetition ad nauseum won't make that point legitimate.
Except we allow statements to be considered as legitimate for tiering, unless something contradicts said statement that is being made. Which is something you've yet to even do. If you're going to claim what Olly is saying isn't true and that he's making it up, it's your job to find why we shouldn't take his statement. Claiming you already adressed something and say you are automatically in the right is not a good argument. Unlike "world", fabric of reality isn't a term that hops from meaning to meaning, what I'm essentially arguing is your own headcanon. Again, it's another term of space and time. That is something you cannot refute. Your example went over specific details that would blatantly mean something else, but it isn't Olly's case.
To put it into perspective on why you're wrong, we'll go step by step on what Olly even refers to and what context.
He states very early on the world will be reshaped into how he wants it to be. World can mean many things in this case. Country, planet, solar system, universe, etc. So we get one of those options.
Next we see the sun is being affected. So that would mean world doesn't refer to anything lesser than just the sun (or solar system technically).
Then we have Olly having a massive grudge for all Toads, stating along with reshaping the world, he really wants them gone too. Toads have existed far beyond the solar system, up to being on multiple different galaxies to even inside different galaxy clusters. Meaning world would chalk off the solar system, or even just a single galaxy.
Finally we have the very fabric of reality. Which again, textbook definition of just another term for time and space. If I've already given evidence for Olly needing to range across several galaxy clusters as a lowball without the final statement, then it's clear to me that this context of space-time would be universal in size by both narrative and general definition. Not like this is the first time Mario had a plot where the fabric of reality meant universe (in-fact this is the second time), as Galaxy already had this same plot where Bowser wants to destroy the fabric of reality to make his own.
Folding the fabric of reality isn't a Tier 2 feat in of itself.
Reshaping all of space and time to your own image would be a tier 2 feat.
Stated by your own tiering system: "Significantly affect" is used as an umbrella term for feats that don't involve direct creation or destruction but are comparable to them in power, such as
warping and distorting the entirety of the structure in question, sustaining its existence with one's own, merging the structure with another one, etc."
The world doesn't automatically mean universe- even if it means more than Earth.
Too bad we aren't using "world" as the main term. It's the very fabric of reality. Which I still have no idea why "space-time" and "reality" wouldn't just mean a universe with it's time. It'd be extremely odd for this word to mean something lower when its main definition automatically lists it as this high.