I disagree. I think a lot of what we do here is more commonly abductive reasoning, briefly mentioned at the end of your post. Although I don't think their explanation is very good.I think that it is important that people understand the difference between Inductive Reasoning and Deductive Reasoning and why Metabunk relies on Deductive Reasoning in examining claims.
But really "reasoning" is sometimes too high level a descriptor for what goes on. Quite often it's just "fact checking".