We can't separate these two things, I agree that in short we will definitely see their latest performance, but I also agree that a big name or history of a team will also have an effect. For example, they are more confident than their opponents and in the game confidence is important.
But on the other hand I can also understand why people say big names or history are not part of it. Because realistically we will see their current situation, that's not wrong in my opinion. It's just that maybe we just have different views, and that's natural.
Confidence is the only thing that matters, history doesn't. If a team was great until 10 years ago, but terrible now, then there is no need to be worried about them. United used to be a great team, but they are terrible for a while now, and definitely horrible this year, why worry about them for example?
History means something if it is recent, like if you were great last year but not doing good this year, but have mostly the same players (like city) then you could say history means something. But if you were terrible last year, and the year before that, and the year before that, then why would you be good this year? This is why only thing that matters is confidence and momentum, the history of a team doesn't matter.