I think I’ve finally totally tracked down the situation in which it happens, in case anyone else has been going slowly insane because of it:
If you copy text, then paste it onto a blank line (that is, an empty paragraph), the result is that you wind up with an empty paragraph before and after the inserted text.
If that’s not what you want (it’s not), and you’re pasting blocks of content (paragraphs, headings, list blocks, etc), just put the cursor at the beginning of the first line of content just before your desired insertion point and then paste. This will paste the clipboard into the document without adding the unwanted <p> </p> lines.