The House of David was a religious splinter/sect of Christianity that peaked in the first half of the 1900's.
They had a baseball team that was kind of like the Globetrotters of baseball that barnstormed during that time.
My guess is Matt Ramsey played for the House of David team, maybe even an exhibition against the Dodgers or Cardinals during that time frame.
Here is a link to a web site of them.
http://www.houseofdavidmuseum.org/sports/index.htm