There is an opinion - fairly wide-spread from what I can see and hear - that the SaaS delivery model implies that consumption is via a vanilla browser.

This conflation of SaaS with the browser is incorrect.

SaaS is a delivery model.

You could enable consumption via a vanilla browser, using technologies such as WPF/E (or Flash), using a rich/smart client container such as the CAB, using Microsoft Office etc - and you probably will enable consumption across the spectrum - depending on the end-user scenario.

The delivery model will not be a moat - and if the the capability you are delivering doesnt have a significant moat - then you are going to have to focus on the user experience to get and to retain the customer.