In this case they do. When you access my API, you're accessing my server, my property. If I have decided that I do not want you accessing that, it's no different than if I have decided I do not want you on my land.
Not everything is special simply because it's digital.
In a hypothetical world in which SaaS has taken over the market, and 3rd-party clients are forbidden by virtue of license agreements, interoperability becomes impossible.
Imagine if Windows Server had been SaaS; Samba would never exist, Mac OS X and Linux couldn't operate in a Windows environment.
Where property law falls down is when we consider what it is you're selling -- access to a service, or a fully controlled end-to-end service agreement where you assert control over both the client and server.
If it's the latter, does this create a healthy market, or does it create something that could never exist before: the ability to create a "natural monopoly" on an individual customer level. That is, once people are invested in your platform, the cost to compete for that person is so high that it creates a nearly unassailable barrier to entry?
Pre-SaaS, if someone wanted to compete with Microsoft Office, they could invest the effort supporting the Office file format to ease customer transition.
Post-SaaS, if Google Docs, Office 365, et al disallow data/API access to third-party clients, supporting your competitors' existing customers becomes impossible.
It depends on why you've decided. If it's by some predetermined rule that applies the same to everybody, it's probably OK. If it's something like "I didn't like that comment supporting same sex marriage you posted on my blog" maybe not. At what point are APIs considered public accommodations?
Not everything is special simply because it's digital.