As has been pointed out, India ink does not need to be fixed in place,
simply blotting will allow the ink to remain.
The rationale for placing the tissue for short time in dilute acetic
acid, acetone, alcohol or various other solutions, is presumably because
the ink is insoluble in these solutions. Most of these inks do contain
gums to permit their adhesion to paper etc. I am assuming that it is the
gums  that are precipitated or fixed in place by the dipping. I am not
sure about this for dilute acetic acid. Acetic acid in the low
concentrations cited should not be able to precipitate gums. The only
time I can recall gums being precipitated was with the use of lead tetra
acetate to precipitate gum of cherry (by Salkind somewher last centrury
..no I did not know Salkind personally!).
If nothing else the dipping is good therapy and may convince the
pathologist that care must be exercised in marking  tissues.
Barry