Maybe not the best example then, but not the only example. If you unintentionally create something that resembles the original too much you may still become liable. It’s hard to draw the line, which is why many in such a position would prefer to be safe rather than sorry.
It’s a gray area, legally. What you say is theoretically correct, but there’s practical issues once you’ve looked at the code that will open you up to legal liability anyway.
For instance, what if you need a utility function during your reimplementation for which there is really only one obvious implementation? You can no longer claim to have come up with it by yourself.
I doubt the FSF would sue over it, but companies are known to avoid the risk.
Because coming up with the same implementation independently is legal, while copying someone else’s implementation isn’t. Which method you used to arrive at your implementation can be difficult to prove either way, which is why it’s important for implementors to be able to say they never looked at the original. It’s a legal defence, in case you ever need to stand in front of a judge or jury who will question how you arrived at yours.