Actually, looking more carefully at this code, it has everything to do with the statement and the matview schema and NOTHING to do with the MaterializedViewFixInfo -- I think that this method should be moved into ParsedSelectStmt and called from there before it calls processMVBasedQueryFix. This change could eliminate the dependency of MaterializedViewFixInfo on ParsedSelectStmt.
If it is handy, ParsedSelectStmt can pre-calculate the group column names (or name to tve map) and pass them into processMVBasedQueryFix.