I don't believe methanol specifically is needed for the reaction to work, the reason it is used is to provide a medium where both the acid and the ketone is soluble. As we all know, the reaction can work in anhydrous conditions using an acid soluble in toluene (tosic acid) too.
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Solubility Chart - "O" means miscible
............MDP2P....H2SO4....Tosic Acid....MeOH..
Water..................O...........O.........O....
Methanol......O........O...........O.........O....
Toluene.......O....................O.........O....