The 20 June release date is mentioned in Ben Rollins' song-by-song notes in the book for the 18-CD edition of The Cutting Edge, under "I Want You".  The date was very likely derived from Dylan's contract documentation, a relevant example of which is shown below. This particular Artist Contract Card is reproduced in the CD-carrying book for the 6-CD edition of The Cutting Edge, and shows three of the songs recorded for Blonde On Blonde.  For each title, it lists all the record releases on which the song appeared, up to 1972; these include C2L 41 and C2S 841, which are the US catalogue numbers of the mono and stereo editions of the album, followed by the date 6/20/66.

Dylan's Contract Card, page 31