Not true. The only common denominator throughout both albums is Jeff Lynne. Jeff produced both albums and played guitar as well. On "Full Moon Fever", the songwriting was mainly collaborations between Petty and Jeff Lynne. Tom asked Jeff to produce his album in 1987 after hearing Harrison's Cloud Nine, produced by Jeff. The idea of the Wilburys was born in mid-1988. The album is rich with Jeff's lush mix of instruments, which is absent in the stripped down Wilbury's albums. The other main players on FMF were Mike Campbell and Phil Jones. George played acoustic on "I Won't Back Down" and that's it; Roy Orbison sang backing vocals on "Zombie Zoo" as part of a group jokingly called "Trembling Tremblers". Other artists on that album are Del Shannon, Jim Keltner, and Howie Epstein. Not a Wilbury combination.
Mystery Girl was recorded in late 1988, at the same time as Wilbury's volume 1. It was released only in 1989 because Roy died in the meantime. Jeff co-wrote three songs. The core personnel on that album are Roy and Jeff. Tom plays acoustic guitar and sings backing vocals on only two songs. George sings backing vocals on one song. Others rest are Mike Campbell, Jim Keltner, Howie Epstein and Benmont Tench and about 20 other guest performances. Again, not a Wilbury combination.
The Wilburys were a true collaborative effort. Everybody sang, everybody wrote, everybody produced - and had great fun doing so. They were friends in real life. That is what makes the Wilburys so unique.