If you're comparing some servers in a 4th tier colo with a poor SLA to AWS and pretending that devops time is free, then sure. But if you're actually building something with comparable reliability and availability, then no way. You're going to spend a lot more than you'd expect on extra capacity, a team of service engineers, load balancers, multiple locations, etc.
This has nothing to do with twitter's reliability. It just means companies have said twitter is more reliable than they are so look for our update on twitter opposed to some company specific system status page.
Your SLA will likely be better than with public cloud.
There's obviously room here though because AWS definitely takes a margin and that means opportunity!