Doctor_Hal said: It looks (from that shot of Whitebeard receiving medical treatment a while back) That Law's symbol was on the I.V. Bottle... and the nurses were his.
Law being Whitebeard's doctor explains a lot.
Well, I'll be able to accept the theory that they're his nurses after the war but WB should be in the New World during that time and Law is entering the NW for the first time with the Straw Hats.