Sure, but if it behaves significantly differently, then I think that precludes it from being a function by function rewrite. At the same time, a component by component rewrite
can be a complete rewrite (but it depends a bit more on the details, I think). If the mainly user visible portions are rewritten, but much of the utility code and other components are not, it may
appear behaviorally different, but but be largely the same code base. It's much harder to know, looking in from the outside.
For a simplistic example, say someone provides a "rewrite" of grep. Maybe the options are all different looking and sounding, so it may appear to be significantly different. But if the core of the matching algorithm and it's capabilities are largely unchanged, is it a that much of a rewrite? To the outside user it may superficially appear so, but to someone comparing the source from before and after, there may be an entirely different opinion, and even that may change if you come from a context of focusing on a particular aspect.
As applied to Trident/Edge, we may have a case where the person speaking was involved in a project to rewrite one major component of the browser, and so is speaking in that context. Maybe that component is responsible for about 60% of the code and functionality, but it still relies on a quite a bit of largely unchanged additional libraries. It's very subjective as to whether you think that qualifies as a rewrite of the project, and depends quite a bit on what was not rewritten, and what you think of that code.