The white points are bases that give you resources. Resources are however capped. So that income allows you to do more for a tick, and maybe a few ticks after. If you're fighting on multiple fronts that can certainly allow another empire to get back in the game (if they're not also fighting on multiple fronts) as your resource spending will be split. It shouldn't be possible to have all the bases and then lose to an empire with none though, as eventually the front will be wide enough that your greater income pushes back.
These were two different scenarios. In harmony, I had captured all the bases except for an outer border and the two colours were fighting back and forth for about a minute or two with no resolution. The other instance was the last level, I had captured the four bases in the middle and the enemy on the bottom with no base was still able to overtake much quicker which I thought was quite unusual behaviour given what I had experienced in the previous levels.