This admittedly distant recollection, related by Johnston to Sony producer Steve Berkowitz, is reported in Michael Fremer's 2013 AnalogPlanet review of the Mobile Fidelity Blonde On Blonde stereo vinyl reissue:

"According to Dylan reissue producer Steve Berkowitz, who oversaw this Mo-Fi reissue and who visited here a few days before this reissue arrived, Bob Johnston told him that in Los Angeles (not Nashville) he and Dylan spent three or four days on the mono mix. Dylan split and Johnston then spent about four hours doing the stereo mix."

Elsewhere, Berkowitz recalled Johnston saying in 1999, "We mixed that mono probably for three or four days, then I said ‘Oh shit, man, we gotta do stereo.’ So me and a coupla guys put our hands on the board, we mixed that son of a bitch in about four hours!"  See this interview with Steve Berkowitz and Mark Wilder.

It seems unlikely that Dylan would actually have sat in with Johnston the whole time, but he evidently had significant input to the changes made.  Both Robbie Robertson and Al Kooper were also reportedly on hand, and may also have had some influence.  Kooper's presence is mentioned in Daryl Sanders' book That Thin Wild Mercury Sound (p.178), and Robertson's in his autobiography, Testimony (p.222).  See Appendix F for detailed references.