You were told correctly, as far as the connections to the Chase Manhattan Bank goes (it was founded by the Rockefellers). I'm not sure about the Alden connection.
The emigrant ancestor of the Aldrich line was George Aldridge (1604/05-1683) and his wife Katherine Seald. They were my 9th great-grandparents. My connection to the line is via George's great-granddaughter Margery Aldrich (1732-1759), who married Joseph White. Their daughter Marcy White then married Calvin Wheelock. Calvin's grandson Henry Wheelock had a daughter named Mary Catherine Wheelock (1851-1923) who married Allen Bates and their daughter Clara Isabel Bates (1870-1950) was my great-grandmother, who married Orvin James Rea.
David Rockefeller is my 8th cousin, twice removed. Considering his agenda, I wish the relationship was much more distant, if not non-existent! If you don't know what I mean, just do a Google search on his name, or, better yet, search for him on You Tube. You'll see what I mean.