Everyone: I’ve got the fix:
Check your browser’s address bar at the top (where your https://blahblah.com address is)
If you’re coming from any site that uses a masked forwarded domain, it won’t work. When you insert media into post while your browser’s address bar has the same domain name in it as the one listed in your blog’s settings > General – WordPress Address URL, it will work just fine.
I tried it with other tabs open, Firefox and Safari. I don’t think it’s browser dependent. The reason for inconsistency is probably from visiting forwarded masked domain sites, coming from frames, and all other sorts of ways in which your address bar will say something besides what it should.
Hope this finally puts this huge issue to rest!