In 1995, through an exchange of EMails, Jim Calvin started working with Peter Lewis of Stairways Software. Peter sent Jim some basic software that implemented a small portion of a news server (along with extensive libraries that Peter used for all manner of products). After considerable noodling around, Jim wrote enough code to implement a moderately robust news server. Jim chose to name it RumorMill (this was during the age of PageMill, SiteMill, and all the other mills).
RumorMill 1.0 was published by Stairways Software in 1996. Stairways continued providing publishing services for RumorMill through version 1.2.2 (late 1999). A long time passed between versions 1.2.2 and 1.3. Jim had been slowly working on version 1.3, including a substantial re-write of the article database. At the same time, Stairways primary product, Anarchie morphed into an even more successful product, Interarchy.
When it came time to publish RumorMill 1.3, Peter and company (Stairways) felt RumorMill didn't quite fit into Stairways current product vision. As such, Jim put together Swaystairs Software to publish RumorMill (RumorMill.com etc. were long gone, so something else had to be used). As you might notice, Swaystairs is an anagram (ok, so there's an extra "s") of Stairways. And swaying stairs are nowhere near as steady and solid as a real stairways.
If using Swaystairs as a name ends up causing too much confusion, the name will probably have to be changed...
If you have questions, you can contact Swaystairs or the folks at Stairways.