So why did the original warning put out by the PHP team say that the exploit didn't rely on the application code and simply having software like Apache mod_php running would be enough?

https://www.php.net/archive/2026.php#2026-10-21-5

You can still trigger DoS. And these can be chained with other vulnerabilites. The expectation of a PHP server executing PHP code also could have been implied.

DoS is independent of the vulns though. From what I understand, you can craft a request of x size which consumes ~200x the memory on the server. Parallelize that and you can DoS servers with only a few GB of memory, even with the 1MiB Nginx limit.