It's CYA time

MS screwed the original update, and it looks to me as if they haven't really worked out exactly what the problem was.
As a result they are - instead of producing a tool to uninstall the original patch and install the new one - providing advice.
If your machine installed the original patch fine, then there is NO need to uninstall it - simply install the new one as a normal update.
If you had problems with the original update, then it's likely that you had to have removed it to get back to a working system. That being the case, then the advice is irrelevant.
I suspect that a few people in MS will be wondering where their next pay-check is going to come from - this problem hit few people, but hit them worse than many other problems that MS have had with other updates. It' more likely that the losers are going to be in the testing area than in the programmer hierarchy, since it seems that a whole segment of users got 'missed' rather than just the (expected) ones with existing system problems.
The part of the article that you quote is actually fairly (maybe make it 'atrociously') badly phrased.
The problem as I see it is with Fonts being installed outside the normal Fonts folder - anything else is likely to cause much lesser problems.
I admit to being under the impression that if you installed a Font, it was automatically copied into the Fonts folder and then installed from there - perhaps I was mistaken, or perhaps there are ways around this that MS hasn't documented.
In short - if you didn't have a problem with the original update, then simply install the new one.
If you did have ANY signs of problems with the original, then yes, you need to get back to a stable baseline before installing the new one.