There's no evidence that the song is anything like old enough to have anything to do with Cathars. The story of the Marys' sea journey to Southern Europe was quite widespread. Also suggested have been thematic links with German 'ship carols' and the story of the Three Kings of Cologne (see, for more on the latter, Anne G Gilchrist, The Three Kings of Cologne (I saw Three Ships), in Journal of the English Folk Dance and Song Society, vol V, number 1, 1946, pp 31-40).

Various notes from the older carol collections can be seen at Hymns and Carols of Christmas: I Saw Three Ships. The link may not work in some older browsers due to the way stylesheets have been implemented.

As Q says, further information is at the older thread, where any further discussion should probably go.