Indeed, the problem goes away with emacs -Q. I investigated further and
found that the culprit is display-buffer-function being set to
popwin:display-buffer. Thus, I can load my current config and evaluate
(setq display-buffer-function nil). The problem will disappear.

I still think that my patch is the right solution. The current code expects
display-buffer to behave in a certain way and Emacs gives us a ton of ways
to change that. Thus, we either need to explicitly set the current buffer,
or we can do away with trying to make *Occur* read-only. And really, who
needs that? Even if we don't set buffer-read-only, the buffer has no
self-insert-command bindings, and if you try to C-k the header, it will
still say "Text is read-only: #<buffer *Occur*>" because there is a
read-only text-property. And why shouldn't you delete matches?

Thus, as far as I can tell, my change makes the code more robust (no longer
depending on display-buffer to work in a particular way) and it has
practically no drawbacks.