Well I don't use Red Hat but when I update Debian Stable, my system doesn't break, and I don't have to pay for 500 site licenses. My system benefits from people that ensure emacs and libre office will work if I update glibc.
The same is not true for Windows, where XP obviously gets dropped with no sane upgrade path and a non trivial cost.
I don't want you to interpret what I'm going to say as talking down to you, but it'll sound that way.
It's clear you've never worked in desktop support if you think that your personal experiences upgrading your computer apply to any kind of wider deployment.
There are issues training staff, maintaining a fleet of compatible hardware, compatible software etc. This all costs money and will - two things Detroit clearly didn't have. Making the software "free" may in some cases bring one cost down, it may also inflate costs in the other parts of the equation.
I personally don't use Windows in my computers, but I have supported networks that do and participated in a Windows XP to Windows 7 upgrade project. You have to hand it to Microsoft, if you stay within their support windows then it's remarkable how well their upgrade path works. The money you pay them is actually buying very polished system.
I think you're both right to some extent. Both approaches have difficulties, just different ones.
The open source approach can have lower up-front costs (but isn't guaranteed to have...), but it requires talent that's harder to find and more expensive as a result. There's also the problem of user resistance, as you point out. We have enough trouble just getting users to use FF/Chrome instead of IE; Linux desktop systems wouldn't go over very well and would require a ton of effort. That's not even touching the problem of a lot of infrastructure being irreversibly tied to software that expects to run in a Windows environment.
But the Microsoft stack can also incur a lot of up-front expenses for larger organizations, and license management isn't very easy either. And, it has its own issues and glitches.
Just to pull a number out of my butt, I'd guess a city like Detroit would be looking at millions in Microsoft licensing costs alone if they were to upgrade their entire infrastructure.
And XP->7 isn't usually too bad, but there are some recurring problems we've encountered (Quickbooks), and XP->8 doesn't work at all.
