The usual way such a thing can occur:
Suppose the top three factions in a system are A (a random faction which happens to be the controlling faction), B (another random faction) and C (a player-group-supported faction). Suppose B and C go to war; faction C is strongly supported while B is not; C's influence therefore climbs rapidly in the war and in the Pending and Cooldown afterwards. Factions cannot be at war with two different factions at the same time, so if Faction C's influence rises above Faction A while they are still at war with B, then a war between A and C cannot trigger and Faction C will end up with the highest influence, but will not yet control the system.
Such a scenario is not stable long-term, as random actions from random CMDRs visiting that station (particularly trading and selling exploration data) will tend to support the faction that actually controls the station. So in such circumstances, unless the player group keeps pushing C higher, then C's influence will fall down until it matches A again, at which point a war will then break out between them. If A only controls the one remaining starport at that point, then the winner of that war will be the controlling faction. If A owns other stations, then this war will be fought with a different station as the prize, other than the controlling station.
The player group may choose to keep backing C until C's influence hits 60%, at which point a war for control will spontaneously start (again, this won't happen if either A or C are already at war in another system).