The chef was telling the truth. Antonio Brown was suspended by the NFL for three games without pay for misrepresenting his vaccine status.
He is one of three suspended by the Tampa Bay safety Mike Edwards and the free agent John Franklin III. We can assume that Brown's suspension has something to do with the accusation from his in- home chef that he had sought out, despite a statement from Brown's lawyer that he is vaccine free. The suspensions of Franklin and Edwards are not yet public, but they seem to be related to the fact that they misrepresented their vaccination statuses to the league. The three will not appeal the penalty.
The answer is that the NFL knew about Rodgers' vaccine status, so they had to pay for it. It is not required for players in the National Football League. The three most recently discovered fabricators probably didn't want to have to deal with the more stringent protocols because they were vaccine free. It is a violation of federal law to create and use a fake vaccine card, so suspension may not be the largest of Brown & Co.'s problems at the moment.
The Wall Street Journal reported that the vaccine card was real, but the information was wrong, which we are taking to mean that he got his hands on a legitimate card but filled out false information. It is not clear if there is a difference between a forged vaccine card and that statement.
The protocols for unvaccinated players include eating separately from the team, staying in the team hotel while on road trips, and submitting to more frequent testing than vaccine players. The strangest thing about this whole situation is that the Packers didn't step in when Rodgers didn't follow press conference regulations for unvaccinated players, even though they knew about his vaccination status. The NFL is fine with rule-breaking as long as they are involved in it.