Religious unit healing

[oedali]

Cyclopedia says "religions units can heal if they are on or adjacent to a holy site in a city that follows their religion". I am finding this is not the case - I am sitting on the holy site of a city state that follows my religion but my apostles are not healing.. is this a bug or intended?

 

[3 EMS]

You might need a temple in your holy district. Mine are healing fine.
I wonder if the pedia is wrong.