Yeah ive seen that, and massive overreaction.
Spoilers for Elseworlds below:
Against Amazo it was Superman they sent for the initial kill blow. Then when he was actually defeated Superman and Supergirl played equal parts in holding him.
The Black suited Superman only began beating the real Superman by putting civilians at risk.
And neither was Supergirl shown to be > Black suited Superman as their eye beam blasts seemed equal.
Talk about the character portrayal or how good the story was, not about a little bit of jobbing to Supergirl on Supergirls own show.
Also they seemed to big up Batman quite a bit with Oliver being intimidated by the idea that he might actually be real. And that was in the Arrow episode.