Twitter was founded in 2006, the same year AWS was launched, so in the early days Twitter didn't have a choice - the cloud wasn't yet a viable option to run a company.
And, if you remember in the early days, Twitter's scalability was absolutely atrocious - the "Fail Whale" was an emblem of Twitter's engineering headaches. Of course, through lots of blood, sweat and tears (and millions/billions of dollars) Twitter has been able to build a robust infrastructure, but I think a new company, or a company who wasn't absolutely expert-level when dealing with heavy load, would be crazy to try to roll their own at this point unless they wanted to be a cloud provider themselves.