Fuzzing is not about modifying data. I don't think that's the right way to describe fuzzing.
It's about testing the durability of a program by trying all kinds of data, as greedy as possible. This includes known problematic inputs and random inputs to match some expectations. By random it can either be totally random (any length, any pattern) or protocol-aware.
Random clicking is a form of random data testing because you are trying random input stream to a program. Your argument is not entirely wrong either. By fuzzing his UI he may trigger the browser to crash. He may trigger his monkey to crash. Fuzzing is a very general technique. I can write a fuzzer that fuzz Firefox's UI Australis. What will I look for? Maybe after opening 100 tabs and closing the 45th tab the titlebar disappeared. Or resize the browser from range s to range w I will find some range will cause the UI to look ugly (style overflow, etc). Or after clicking on the scrollbar several times consecutively the browser crashed.
Barton Miller, the "Father of Fuzzing" did UI fuzzing by simulating actual keystrokes and mouse clicks. See ftp://ftp.cs.wisc.edu/paradyn/technical_papers/fuzz-nt.pdf
In his Forwards page, he even mentioned "Monkey" http://pages.cs.wisc.edu/~bart/fuzz/Foreword1.html