tl;dr: Clear your (Comet) Cache!
Long answer:
I only have 2 words: Comet Cache!
Comet Cache was enabled.
Checking the source code showed me a note like this, after the closing </html>
:
<!-- *´¨)
¸.•´¸.•*´¨) ¸.•*¨)
(¸.•´ (¸.•` ¤ Comet Cache Notes ¤ ´¨) -->
<!-- Cache File Version Salt: n/a -->
<!-- Cache File URL: http://<my-domain> -->
<!-- Cache File Path: /cache/comet-cache/cache/http/<my-domain>/index.html -->
<!-- Cache File Generated Via: HTTP request -->
<!-- Cache File Generated On: Feb 22nd, 2017 @ 5:37 pm UTC -->
<!-- Cache File Generated In: 4.59149 seconds -->
<!-- Cache File Expires On: Mar 1st, 2017 @ 5:37 pm UTC -->
<!-- Cache File Auto-Rebuild On: Mar 1st, 2017 @ 5:37 pm UTC -->
<!-- *´¨)
¸.•´¸.•*´¨) ¸.•*¨)
(¸.•´ (¸.•` ¤ Comet Cache is Fully Functional ¤ ´¨) -->
<!-- Loaded via Cache On: Feb 22nd, 2017 @ 5:37 pm UTC -->
<!-- Loaded via Cache In: 0.03472 seconds -->
Manually deleting /cache/comet-cache/cache/http/<my-domain>/index.html
(path relative to your /wp-content/
directory) solved the issue.
I feel so stupid for assuming that there was no caching going on. Always blame the cache!