The turn decorating each eighth note can be played literally. Except for the one on bar 179's A sharp, because there's no good candidate for that turn's lower auxiliary note. G natural is too low. G sharp is harmonically bogus. G double sharp is Chopin, not Beethoven.
So should the B - A sharp with turn be instead simplified into a B with turn, where A sharp is the lower auxiliary?
Should the dozen similar instances also be simplified thus?
I prefer arguments stronger than so-and-so recorded it like such-and-such.
Edit: A turn with a tiny sharp underneath occurs in bar 27 and in bar 161, both in the Henle and in the first edition (p. 32 bottom, p. 36 middle; although here the sharp is above, not underneath). Had Beethoven wanted the Casella interpretation, he would have notated it that way too: a quarter note B with a turn plus sharp. So we can't explain the Casella as a modernization of an archaic spelling.