I believe you are wrong. I also would be willing to see evidence to the contrary.
This has been hashed out before, but never addressed specifically by anyone at the league.
The relevant section is Article 50.10 d) iv) Page 290 of the CBA.
There is a requirement that a player must be deemed unfit to play to be placed on LTIR, and a requirement that once the player is returned to the active roster, the team must be cap compliant.
But there is no restriction on a team regarding when they are required to return a fit to play player to the active roster.
From that section
"A Club may then exceed the Upper Limit due to the addition of replacement Player Salary and Bonuses of Players who have replaced an unfit-to-play Player, provided, however, that when the unfit-to-play Player is once again fit to play, the Club shall be required to once again reduce its Averaged Club Salary to a level at or below the Upper Limit prior to the Player being able to rejoin the Club."
Note that they specifically mention that when a player is once again fit to play, the team must become cap compliant before they can bring him back. NOT that the team must bring him back immediately, or are not cap compliant the moment he becomes fit to play.