I think you are confusing the Hillary campaign server, which the FBI did not see and Hillary had Crowdstrike working on and the DNC servers which the FBI did see and look at in the DNC offices. I believe the DNC servers were mirrored by the FBI as I recall but were kept up and active.
I agree with you that Hillary would try to steal the election. I doubt the DNC staffers in general thought that she would. They have undying loyalty to the top cadre such as Hillary.
**Flash Back***
Director James Comey said last year that the DNC had denied the bureau’s requests to examine the breached servers.
Comey said at the time that the FBI and DNC agreed to let a private firm access the servers and share the findings with investigators.
http://thehill.com/homenews/administration/388507-trump-why-didnt-dnc-hand-over-hacked-server-to-fbi