No. I am on Lemmy.World right now viewing a KBin thread. My entire interaction here is through Lemmy.World and not KBin. So for me to say, “I was on KBin arguing with someone,” would be factually incorrect because I am not on KBin. It would be factually correct to say, “I was on the Fediverse arguing with someone,” but since the Fediverse has different forms, that interaction itself could take several forms and context does sometimes matter. There’s nothing wrong with the more generic The Fediverse, but there’s also nothing wrong with stating which instance you’re using to be more specific.