First of all, the word “banned” was used by The Hill. I doubt very much the Trump admin said anything stronger than “suggested”.
But “banned” makes it sound like evil censorship (the usual demonizing) and attracts more readers.
Secondly, controlling the language is something the left has been doing for years . . . but when the right tries it, it’s evil, or otherwise fraudulent.
Joe Sixpack’s thinking is heavily influenced by the words that are used (pollsters use this fact all the time) . . . hence the left’s word control.
A little pushback in this arena is long overdue (and the left doesn’t like it . . . hence the article framing this as censorship).