Spring Integration goes way beyond just Web Services.
Integration has lots of parts, than just one type. There are things like routing, splitters, aggregators, claim check, inbound, outbound adapters for File, FTP, JMS, AMQP, Http, RMI, to name a few. Also Gateways, and filters and enrichers. And that you can write and design and modify/add in many cases with just a change to configuration and no code.
So "etc to handle most of the integration part" quote is looking at a small portion of "Integration" is.