(I also responded to your question on the Organic Gardening forum)

It's doubtful that ants are doing the damage. I suspect that what's happening is that some other insect or pest is causing the damage to your tomatoes, then the ants are getting in, and that's what you see when you look at the tomatoes.

Or, the fruits are cracking (either radial or concentric cracking), again providing the ants a means to enter the fruit.

radial cracking

concentric cracking

Can you describe what the eaten up spots look like? How big are they? On the tops or bottoms of tomatoes (or random)?

By the way, peak harvest times for tomatoes in Texas are mid May to early July, depending on what part of the state you live in. Fruits in July, especially late July, are generally not of very high quality due to stress on the plant from extreme heat, as well as pest and disease pressure.