According to this bio of Truman's grandmother Mabel K. Persons, Truman;s grandfather was a unerversity professor. Not likely he went on to be a professional ballplayer:
http://jacksonville.com/tu-online/st...20792490.shtml
Although grandma Mabel, according to the article, did live for a time in Havana, with her two youngest sons, all three of her sons appear to have been born in Alabama, including her eldest son who was Tru's father. Tru's mother Lilly, in later years, married a Cuban businessman, Joseph Garcia Capote who adopted Tru and whose name Tru took, thus likely explaining the erroneous claim that Tru's father was born in Cuba.