It's not naive at all. Especially when other teams could challenge if they think something is sketchy. Lying and making a false medical diagnosis can cause a doctor to lose their practice licence for some time. No doctor will risk that just so a team can have a better chance at winning.
If you've worked in the medical field, you'll understand one thing though : doctors are very reticent at taking any sort of risks, unless the situation calls for it (life or death situation, potentially avoiding permanent damage, etc). There is not a set magical point, as I said, where a player suddenly goes from being unable to play to being able to play.
Can some teams plan surgeries so that the recovery time falls in line with the start of the playoffs, absolutely. Tampa has done it, notably. But the league is in no legal position to decide when a player has to have surgery. If the player is willing to wait for said surgery, there is nothing the league can do that wouldn't be illegal.