I don't think Amazon really provides any products that are going to prevent you from hiring staff. That's the domain of companies like Zendesk or Salesforce.
All they provide you is the bare metal in easily-purchasable quantities. Whatever time you saved not having to lug a server up to your datacenter and plug it in will be spent debugging CloudFormation stacks or figuring out how to auction off your reserved instances that you no longer want.
Obviously you'll still need some staff. But suddenly you don't need staff that knows how to handle physical server rooms and data centers, you limit it to AWS which covers a whole range of needs which would need to be addressed by different staff with different skillsets.
I think you read too much into that comment. AWS didn't have to market the fear into the customers. People are naturally afraid of things. AWS does provide value, but it comes at a steep cost.