Rodgers took some sort of alternative to the approved vaccines and he applied to the NFL for that to count as him being "vaccinated". He did not lie, because he did not say he had taken a vaccine. Also there is nothing wrong with lying to the press, they lie to us everyday!
The issue here, is when did the NFL rule that Rodgers can not be treated as a vaccinated player? I'm guessing from the speed of the cover-up, it was as soon as he tested positive. As much as I would love to see Rodgers and the Packers fined, have draft picks docked, put into the stocks, laid bare and marched through the streets of Green Bay followed by a priestess banging a drum screaming "shame", none of that is going to happen, because the memo that the NFL put out only spells out consequences for the team and unvaccinated player if a game is cancelled.
From my reading of the memo, if the league did deny Rodgers request before the preseason, the he and the Packers violated the leagues protocols which the NFL could then withhold the $2.8 million they are giving each club to help cover the costs of the COVID protocols they put in place.