Your assumption is correct. It will show up as an option, but only if you click on the "Customize" button that appears before the installation begins. I haven't installed Leopard yet on anything, so my information is based on Tiger and earlier. However, I'm sure the selections should be the same in Leopard.
I usually prefer a fresh installation as well, even on my Macs, but there comes a time when that's not an option even in the Windows world. I personally use that as a last resort option, since it might involve leaving the user without applications that they had once before. It's assumed that the user would have kept the installation discs for the apps, but this isn't always the case. Still, a fresh installation does rule out problems that might have been there before. Thankfully, A&I also does this without being extremely destructive.
Usually with applications on the Mac, the applications are self-contained (they're actually
"executable folders" if you look closely), meaning they shouldn't be leaving traces of themselves in other places of the operating system (as Windows does with DLL files). This means that installing apps and deleting apps on the Mac is as simple as dragging the app icon to the Applications folder or to the Trash, respectively. You don't necessarily need to have applications residing in the Applications folder for them to work, either. One can easily drag an application icon over to one's home folder or another drive and it will work without a hitch.
The only time something might arise is if the application was put in there by an installer, specifically one that has a tendency to treat the Mac as if it were Windows by installing files in places other than the application bundle itself. This is a rare instance, but it does exist unfortunately.
I recommend doing an A&I and see if things get better on her Mac. If the problems still exist, then it might be time to start from scratch.
Incidentally, Time Machine might be another way to revert things back to when things were working, but she might lose any files created or apps installed after that particular snapshot, possibly even updates installed since then. I haven't played with Time Machine, but I assume these are things to consider.