I've heard at least three different versions of why they chose that symbol:
1. It's really not a Star of David but two triangles, one black and one white, symbolizing the joining of the two brothers in a business venture. Possibly each triangle symbolizes a Greek Delta, for the first letters of their last names.
2. They weren't Jewish, but it was chosen as a symbol to tick of Henry Ford, who hated Jews. (If you're ever around Detroit there's a little suburb named Inkster. Legend has it that the name came from Ford because of all the blacks living there.)
3. One of the brothers was a law enforcement fan, and since Sheriffs since the old West had worn six-pointed stars that was chosen as the symbol for Dodge.
One, two or all three, who knows?