Salesforce integration all-or-nothing

We have a customer who makes use of Salesforce after joining Salesforce Course, but they want to develop their own site which will perform a multitude of functions some of which would require integration with Salesforce data and functionality.
In discussions with a Salesforce vendor and our customer, the Salesforce vendor pushed for the customer to do everything in Salesforce itself, as in a portal solution where their entire website is run through Salesforce, or you would switch from some basic HTML pages on your own server to Salesforce pages (Skinned to look like the customer's site).
Surely this recommendation is not in the best interests of the customer?
Doesn't this restrict and limit you to Salesforce technologies and costs?
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Our application is rut on our own servers and infrastructure. We do not run anything on Salesforce infrastructure. We send data to Salesforce through their API.