In my experience the cost savings are because people assume that AWS means "I dont need Ops (any more)" and have developers with zero ops/sysadmin experience running their production environments.
That being said, it can burn you. For an ETL platform I was developing cobbling it together with Lambda and other services was a nightmare. Things you'd expect to work didn't. And the cost was way too high for concurrency. So I went back to a single box with beanstalkd and common tools.
But I agree many go with a promised solution without the expertise and when it fails or gets hacked they're screwed. And those costs aren't factored in.
If we're not hosting and maintaining and the client doesn't have skillset in-house I'll have a client go to Rackspace or similar.