I have actually built and scaled a system similar to Twitter called Plurk (which has millions of users, billions of data items and similar use cases as Twitter). We built this with a team of a few developers and one sys-admin. While Twitter is at a much larger scale, I really doubt you need 1000 engineers to solve that problem, because even at Plurk's scale we built automated systems for scaling, monitoring, backups etc. (e.g. sharded the databases, used master-master MySQL setups that supported auto-failovers, nagios for alerts etc.)
You may say: but they have mobile apps? But so do a lot of other companies that don't have 1000 engineers. You need a few really great mobile devs to build great mobile apps, again based on my experience.
I think what has happened for them is that their structure isn't that good and they have scaled too fast (and in this process they have hired a lot of B and C people that aren't that good). It's a least my conclusion based on the limited information I know about them.