Their software and services exist to differentiate the hardware and allow for a profit margin.
The Microsoft corollary would be if Apple offered iTunes, iCloud, etc for Android.
How is a company that makes OS X, iOS, iCloud services not a software company? Sure it sells hardware, but not hardware that's a brick.. People buy the hardware so they can use the software which pretty much means they sell a package that includes both hardware and software..
This is a useful way to understand Apple, but not companies in general. Movie theaters make the majority of their profit off of concessions, but they are not popcorn companies.
For what it's worth, I get your point, though. My preference is to use OSX over Windows these days, but that's because I find it to be the best intersection of *nix boxes (which all of my servers run) and a pleasant UI with great apps (because I'm still a human, and sometimes I tire of the command line). But look at the way iCloud took forever to become stable - if it's even there now - or the recent decreased in perceived QA (iOS 8.0.1, Apple Maps), and you can tell Apple's focus isn't on software as much as hardware.
I believe Apple is a product company. They make things that people want to buy and use. Their products are built from a combination of hardware and software/services.
Microsoft is also a product company. The difference is that they make a lot of different types of products. Some are things people buy and use like Xbox, Surface, and Lumia. Some are "platforms" like Windows and SQL Server. And they still sell "software" like Office.