Unless the sun was VERY close, the actual distance doesn't matter. What matters is that the sun (or a star, or whatever you use as a reference) is so far away that there is no practical difference between "far away" and "even further".

For practical purposes, we treat the sun as being an infinite distance away, and the error caused by it being ONLY 93,000,000 miles away is much smaller than Eratosthenes could measure :)

It's similar to drawing perspectives, you draw perspective lines to join at the distant horizon. You don't care how far to the distance horizon.

(Those ancient Greeks had amazing understanding of geometry. Much better than most of us.)