Boxee generally uses details from thetvdb.com and not imdb.com for TV shows. Using thetvdb.com details I haven't generally had problems with Boxee identifying the 1963 Doctor Who.
Here is the page for the 1963 version:
Here is an example filename for one of my episodes - which just happens to be the first part of Shada with Tom Baker:
Doctor Who (1963) S17e21.mkv
I did find that sometimes Boxee would misidentify an episode of the 2005 show as one from the 1963 one. To resolve this I created an NFO file called tvshow.nfo in the folder for the 2005 show, containing the following (78804 is the id for the 2005 show on thetvdb.com):