Thanks for your question and your excellent photo about tomatoes rotting. As you have already figured out, this can't be blossom end rot.
I have a few questions for you:
Are the tomatoes that have this problem touching the ground?
Are all the tomatoes on the plant affected?
Are the leaves on the plants affected normal-looking? If not, what do they look like?
Since I can't feel the tomato myself, is the rot firm and smooth on the outside, or is it squishy?
On the inside, what does the rot look and and it is hard or soft?