>"It is important to note that the university did not deny the First Amendment rights or academic freedom of professors Dan Smith, Michael McDonald and Sharon Austin," the school said in an email to NPR. "Rather, the university denied requests of these full-time employees to undertake outside paid work that is adverse to the university's interests as a state of Florida institution."
The operative phrase there is "outside paid work."
I believe you interpreted NPR's article exactly the way NPR intended you to interpret it. That is to say, you were supposed to read it and walk away misinformed due to the framing.