My basil plant has developed small black spots with star shaped light grey areas around the spot on the leaves. Also there are tiny black specks on some leaves that look like droppings. Some of the leaves look as if they have been chewed also. I think these are two different pests. I am in southern Baja where it is hot right now. I follow watering, feeding and sunshine instructions. I read somewhere that the black spot with star shape around is actually a very tiny worm and can't be irradicated. Please someone help, I love my plant!
Can you take a leaf with spots and a razor blade to carefully cut the spot open? If it is a leaf miner you should be able to see either the larvae (worm) or evidence insect babies were there. I've never heard of a 'worm' that is not able to be controlled. Eradicating anything in the plant world is rare and always contraindicated (not a good thing, not a reasonable goal). Leaf miners are easy to control...but without a positive ID 'trying' any product is wrong.
From what you are describing it sounds more akin to 'shot hole' by a common fungus. Common to a huge number of plants. When a spore in a drop of water lands on a leaf the plant will surgically remove that particular spot leaving a hole. The plant is taking care of itself and needs no further help.
That grey ring sounds exactly like the plant is killing its own tissue around that spot to get rid of the spore/fungus. Just drops right out of the hole falling to the ground. Similar to taking a pair of scissors or exacto knife to cut out the black spot. Cool, huh!