I would find a different eye doctor, honestly. The rubbing explanation sounds iffy to me and I would be concerned about a test not being completed.
In our case, we had our DS tested and learned he needed glasses for farsightedness when he was four. We were told it was a big correction. We moved, took him for a checkup in a new town, which turns out to have a well-known ophthalmologist with a specialization in pediatrics. Turns out DS' vision was under corrected by about twice what he needed! He also needed patching for a few months. We are really glad that we were forced into another doctor because the first one, though nice, wasn't completely accurate.
