You are correct, but consider:

- global OSM requires that `amenity=clinic` must also get `healthcare=clinic`
- we don't seem to agree what tag-values to represent "clinic grounds" (e.g. `landuse=institution` is discouraged by global OSM; look at Mong Kok Police Station and it's also `landuse=institution`)

I see e.g. Robert Black Health Centre is currently tagged as a `healthcare=hospital`, which may be an interesting approach to the "clinic grounds" problem.