The majority of shares are owned by the fans, Kibble are a large minority shareholder and many shares lie in the hands of members of the public who may or may not be saints fans. That means we are partially fan-owned, not fully. When Gillespie was at Kibble it was him, the chairman and Lasley who ran the club's business.
I'd say that up until Gillespie's departure Kibble were the group that really ran the club, maybe that is still the case.