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?
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.
I think we can agree the statement makes the implied assumption you still do have a reason to run PHP. It doesn't matter what application needs PHP, as long as it's an application needing PHP. Delivering a static webpage is not a reason to run PHP, that's webserver biz. I mean, c'mon, it's bug in the PHP backend, not the OS where the string "PHP" magically causes memory corruption. Something needs to be processes by PHP.