This is just approval by the FIA. Formula 1 itself also needs to approve it, and a lot of teams don't want to accept a new team since it dilutes the money prizes for the constructors championship.
Was the theoretical case of FIA approving and "Formula 1" (FOM?) Not approving the one where they'd technically be allowed to race, but them racing would not be allowed to be broadcast?
That is the situation, the problem with that is: if Andretti/ Cadillac come in and do well enough to score 9th or 10th then either Williams or Haas get no money and likely go out of business. Whereas currently 10th place gives them just enough to stay alive
I suspect it actually means redistributing the season payouts over 11 teams instead of 10. Otherwise it would be impossible to fund the teams that come in 11.