I'm 100% confident that wasn't the case.
Dozier >>> Forsythe and everyone knows that, Twins wouldn't have picked up the phone again if it was just JDL for Dozier, there is a reason why they included Alvarez, Dozier is in his prime, 45+ hr power and a 5-6 WAR 2B
Forsythe is pretty good, really solid OBP and has slugged .444 the last two years with an ops over .790 the last two years. Really solid defender too. Dozier definitely the better base runner though.
That being said, Dozier isn't better enough to justify DeLeon + Alverez+ more compared to Forsythe, while he would be an upgrade over forsythe, he isn't enough of one to make up the difference in price.