Web Services, at its essence, is a loosely couple distributed object platform, something that we have been leveraging within EAI problem domains for years. WSDL, for example, looks a lot like CORBA's and COM's IDL, and IIOP functions a lot like SOAP. Web services perhaps are just a better more open way to create and implement distributed and integrated applications, with simplicity of standards being the primary benefit. I think Web Services are a great step forward.
Web Services provide method level access to applications, allowing application integration architects to bind applications together at the application service level (e.g., an exposed function), creating composite applications that are made up of many remote applications. In doing this applications are integrated, in fact they are coupled. This is an existing practice; Web Services is just new enabling technology and set of standards.
To answer your question directly, EAI and Web Services are joined at the hip. EAI has always employed application service binding mechanisms (e.g., see my chapter on "Method Level EAI" in the book Enterprise Application Integration, 1998), including CORBA, COM, J2EE, etc., Web Service is just another tool in the EAI shed. If vendors are trying to promote Web services as something that does not belong in the world of EAI, they are indeed misinforming end users.
This was first published in January 2002