It's believed that it would be cheaper for Twitter to have used cloud services (Snapchat spends less then they do on data center operations).
There are certainly examples for big companies that benefit from having their own infrastructure (i.e. Dropbox since they have relatively specialized hardware needs compared to what cloud providers set prices around), but the number of people you need to hire to build and maintain datacenters is very high.
Twitter initially ran everything in the cloud. I should know, I was employee 13. It was much cheaper to build our own server hardware and move to our own server and network agreements. Peering and transit is cheaper at scale, as is commodity hardware.
Those numbers have changed since you left. And they could change again. It's all dynamic: these comparisons and the economically and strategically "correct" choices change over time depending on talent availability, demand, speed of scaling requirements and so on.
There are certainly examples for big companies that benefit from having their own infrastructure (i.e. Dropbox since they have relatively specialized hardware needs compared to what cloud providers set prices around), but the number of people you need to hire to build and maintain datacenters is very high.