in many cases can reduce your network costs, increase bandwidth throughput, and provide a more consistent network experience than Internet-based connections.
The costs you reduce are the Amazon network bandwidth charges for accessing the Amazon cloud -- instead, you pay for the same provisioning.
The latency they talk about is the access from customer premises to Amazon data centers. If you buy dedicated connections to their data centers from customer premises, it will side-step the "local ISP" problem. Which is reasonable for a company that has a facility close to a local fiber loop, but kind-of dies when you try to do it for each end-user customer in an area.