Solve for the Fairfax County third dose equilibrium

I am genuinely unsure how this one is going to play out:

There is no proof of medical condition required to receive a third dose of vaccine at one of the Fairfax County Health Department vaccination sites, and individuals will not be asked to provide medical documentation.

Then there is this insanity, for people who in expected value terms need it most:

There is not enough information to recommend an additional vaccine dose for people who have received the Johnson & Johnson vaccine. Studies are currently underway to evaluate the protection provided by the Johnson & Johnson vaccine to people with weakened immune systems. Recommendations for these people will be coming in the near future. The Centers for Disease Control and Prevention does not recommend that people with a compromised immune system who have received a dose of the Johnson & Johnson vaccine start a new vaccination series with Pfizer or Moderna.

But I guess we’ll be telling them something different a few weeks from now!  Or maybe not.  Here is the cited press release.