Well, it's not an exhibition game against the Boston Red Sox. The Tigers visited Fenway Park for a series against the Sox starting on that date.
That only leaves the Memphis Red Sox of the Negro League. The only other Negro League team that I can find that used the name Red Sox were the Cleveland Red Sox and they disbanded after 1934. A local team in Indiana could very well have hosted the Monarchs for a game. Could be either a semi-pro or minor league team.
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