I've never quite understood that justification.
How much meaningful compatibility testing can a sysadmin actually do? Granted, they should have better-than-anyone-else knowledge of what software is in use within the company, but they know next to nothing of the day-to-day use cases for that software, let alone the edge cases.
Example: I use a piece of software that outputs documentation, using MS Word. When Office was upgraded from 2010 to 2013, this software broke. Not immediately - it only breaks when outputting a large (>300 page) document, and it took me several days of experimentation (and some months of exploring workarounds and compromises) to be sure of the cause. Sysadmins didn't have a clue about that, and I wouldn't expect them to - their role is limited to "giving me the option to roll back to Office 2010". (Which they did, when I moaned loudly enough.)
So sysadmins sit and test every patch in a Windows release? Yeah, right. Sounds more likely to me that they'll boot up every program once, then spend another hour on tech news sites looking for people whinging about functionality broken by the update.