Virtually all of the code is open source. There are also alternative implementations. So yes, right now, it’s run by them, but they can’t hold the community hostage: if they start doing bad stuff, the community can easily fork.
Ah. I thought (perhaps hoped) you were referring to something more. I think decentralization of the actual data and infrastructure is the key. OSS is necessary but not sufficient. If Twitter were open sourced and widely forked tomorrow, not much would change, since Twitter still holds all the tweets and hundreds of millions of users.