How do you make sure that the refactored class does the same thing as the old one? Rewriting old code that you don't have test coverage for is way riskier than whatever small change you were going to make to it.
I write a lot of code without tests because a lot of legacy codebases aren't set up to be testable, but they work, and it's important to the business that we're able to deliver small bug fixes and incremental improvements on the existing code while we write whatever replacement system we want to write. As I work on them they'll slowly get more testable, but if you're abandoning working code because it has no tests, you're usually making the wrong decision. (Which the author recognizes.)