That reads to me as 'Twitter the organization', not 'Twitter the people in the organization'. I suppose it could be either, but I have never heard that kind of wording for a company as its constituent employees instead of as a monolith. I am open to a different interpretation if you can guide me through it and it seems plausible to me, but if there is no reconciling the disparate readings then I suppose we shall have to admit to an impasse.