The reason that it's lying is that natural immunity does provide decent protection. You're so focused on incentives in the small that you forgot about incentives in the large -- this type of bs is exactly why people feel entitled to opt into believing "alternative facts".
Natural immunity and vaccination provide even better protection, though. Plus vaccination can help with Long COVID symptoms. So I don't see that there's anything wrong--or misleading--with encouraging/requiring people to get vaccinated to avoid weekly testing.
"Lying" implies malicious intent. It is not lying to communicate via the channels of public health the strategies that would optimize our utilization of public health resources.
As we are literally seeing in many states, obtaining natural immunity en-mass means that ICUs fill, doctors and nurses burn out, and morgues have waiting lists.
That "natural immunity provides decent protection" is itself a lie. Decent protection for whom exactly? It doesn't protect your community to act as a vector for this virus while you are obtaining said immunity. It doesn't even protect you from the risk of long-lasting post-infection disability. It is deliberately malicious and puts its believers at an objectively higher risk.
Are you really sure you want to go down that road? Are you really saying you're fine with someone telling you falsehoods so long as it's in what they believe to be your best interest?
It is not lying to communicate via the channels of public health the strategies that would optimize our utilization of public health resources.
Is the strategy actually working? It sure doesn't seem like it. In fact, it seems to be eroding trust in public institutions on a massive scale with very little other benefit.
"natural immunity provides decent protection" is a falsehood that exposes your intentionally limited definitions of "decent" and "protection." Again it is anything but decent behavior to expose your community to a contagious virus and it doesn't protect the person desiring immunity via infection from potential disability. Natural is even in question as the mechanism by which the body produces antibodies against the virus is the same. The RNA vaccine encodes a specific antigen, this antigen is presented to your natural immune system and it produces defenses like it would to any other antigen.