This is not true at all. The hard part isn't cloud vs. on-premise, it's the architecture.
Most sites can either put all their data in a single massive database, or else have an obvious dimension to shard by (e.g. by user ID if users mostly interact with their own data).
But sites where the data is many-to-many and there's a firehose of writes, of which Twitter is a prime example, are a nightmare to scale while remaining performant and reliable. Every single user gets an updated live feed of tweets drawn from every other user -- handling millions of users simultaneously is not easy.