You are confusing the former gov (Brereton Jones) with Eight Belles’ trainer (Larry Jones). Not related. Brereton had nothing to do with Eight Belles.
There is a happy connection between the two Joneses: Brereton Jones is the breeder/owner of Proud Spell, the filly who won the Kentucky Oaks at Churchill Downs on Friday. Proud Spell is trained by Larry Jones. The filly owned by Brereton survived her race.