Emphasis mine:

- Wikipedia: Software as a service is a software licensing and delivery model in which software is licensed on a subscription basis and is centrally hosted.

- Dictionary.com: Software as a Service: a software distribution method in which a service provider gives customers access through the Internet to applications, usually ones developed and owned by the provider

- techterms.com: Stands for "Software as a Service." SaaS is software that is deployed over the Internet rather than installed on a computer. It is often used for enterprise applications that are distributed to multiple users. SaaS applications typically run within a Web browser, which means users only need a compatible browser in order to access the software.

- Salesforce.com: Software as a service (or SaaS) is a way of delivering applications over the Internet—as a service. Instead of installing and maintaining software, you simply access it via the Internet, freeing yourself from complex software and hardware management.

Sure, desktop apps can be subscription based, but that isn't the same as SaaS. The second S in SaaS is "service" as in, you are providing something more than just the software. With your example of Office365, there is a web based component, and the accompanying storage to go with it.

So given that the post I replied to, was suggesting a desktop app because a previous solution had "moved to the cloud", I maintain that there is confusion about what SaaS means.