No, they way you used deductive logic is right, but your premises didn't include how software [the OS, in this context, based on your link], hardware are manufactured and integrated.
Usually, hardware is manufactured in sterile environments [remember those and back and forth arguments/discussions about manufacturing chips in the movie Disclosure? Something like that.] With H/W, while they are being manufactured and assembled, there are two states - the combined product either works, or it doesn't. All faulty components are sent back to testing, or they're destroyed, so ultimately the "machine" that comes out HAS to be working. After the machine reaches the end-user, H/W failure is usually related to how the user uses it. For instance, too much dust settling in some of the parts can damage the system, and cause a crash. The DVD drive, for instance, is usually the first to go in most systems, simply because it's exposed to dust and other particles that might affect it's functioning.
The software, on the other hand, goes through regular development and testing cycles, however, there are several places where the programmers could go wrong. They could miss handling certain error conditions; they could over look handling certain program behavior; memory faults; memory/buffer over flows - there are several such issues that programmers continuously over look even after 30+ years of developing Operating System software. Developers of Unix/AIX/Linux based OS are able to successfully overcome these mistakes - at least that has been their track record. Attribute it to how they develop their software.
So given that there are so many errors [like those you'd come across in Windows based systems] that are still left unchecked when the final product is churned out to the end user, it's not surprising that there are more software crashes than hardware crashes. Crashes that don't have to do anything with what users do. This is what causes so much frustration among users, particularly for those users who are still dependent on "user friendly" Windows based systems.
Your article discusses several such issues caused solely by software issues like looping, deadlocks, and overflows.