Setting permission rank will not apply on chests and other functional blocks. This is fine for most but having your chests accessible to every faction member is not recommended.
A possible solution would be to implement a second permission rank that you can select on each chest or some sort of password system (link a display module to a chest?). Each chest would have his own permission rank requirement, allowing factions to have several chests on 1 entity that is each accessible for a select group.