Problem is most common with the pedals adjusted well aft (for shorter pedalers) which tips the drive spine forward if holding by the pedal shafts.
I can't imagine a fin falling off in this manor by simply installing the drive. It takes considerable torque to pull the brass nut through the fin. May have been another cause or hanging loosely from a previous outing.
Fyi... Hobie Mirage Kayaks are coming with a drive alignment pin feature since 2012 model year to help prevent mis-aligned drive installation. Way easier now.