The Battle Ops Manual that comes with the Japanese special edition of the game not only expressly states that the game has no story, but it also clarifies that 'Umbrella Corps' is just a term for anyone who takes part in the battles, irrespective of corporate mercenary or civilian thrill seeker.
We know that the Grim Reaper and other employees followed directives from an unnamed organization to which they were subordinate. Even without Douglas the hints are too strong that Wesker may be the leader, because even his title in the organization is a reference to Resident Evil 5, where Wesker obtained status, wealth and honor after taking over a rival company. We can't know for sure yet whether Wesker is really alive or dead, because it's not reliable now.
Moreover, in multiplayer, we can also hear the voices of employees who talk about the resurrection and the imminent changes in the world because of them. What do they refer to, if not Blue Umbrella?
Even both the Umbrella Corps and Blue Umbrella logos have their diagonal sides painted over, similar to the remnants of Umbrella Corporation symbol from Resident Evil 4.
Let's add to that the fact that Umbrella was reorganized a year after the Umbrella storyline was abandoned to get a number of suspicious coincidences.
I'm sure you've heard these arguments a myriad of times, but the idea that there are two illegal organizations in the Resident Evil world, linked to Umbrella and Wesker, that have the same goals, but that are unrelated to each other, seems absurd, to be honest. I am more than sure that Wesker was "resurrected" in the first place to hint at the connection of these storylines, since they are strictly associated with him.