At the risk of irritating you;
You're asking the wrong question. You don't need a reason NOT to deviate from the defaults, but the other way around. You need a reason to do so. Timeouts are absolutely essential when running a web server and to disable that setting without a reason is inherently contrary to good practice, even if it's running on a web server that happens to have a timeout directive of its own.
Now, as for the real answer; probably it doesn't matter at all in this particular case, but it's bad practice to go by the setting of a separate system. What if the script is later run on a different server with a different timeout? If you can safely say that it will never happen, fine, but good practice is largely about accounting for seemingly unlikely events and not unnecessarily tying together the settings and functionality of completely different systems. The dismissal of such principles is responsible for a lot of pointless incompatibilities in the software world. Almost every time, they are unforeseen.
What if the web server later is set to run some other runtime environment which only inherits the timeout setting from the web server? Let's say for instance that you later need a 15-year-old CGI program written in C++ by someone who moved to a different continent, that has no idea of any timeout except the web server's. That might result in the timeout needing to be changed and because PHP is pointlessly relying on the web server's timeout instead of its own, that may cause problems for the PHP script. Or the other way around, that you need a lesser web server timeout for some reason, but PHP still needs to have it higher.
It's just not a good idea to tie the PHP functionality to the web server because the web server and PHP are responsible for different roles and should be kept as functionally separate as possible. When the PHP side needs more processing time, it should be a setting in PHP simply because it's relevant to PHP, not necessarily everything else on the web server.
In short, it's just unnecessarily conflating the matter when there is no need to.
Last but not least, 'stillstanding' is right; you should at least rather use set_time_limit() than ini_set().
Hope this wasn't too patronizing and irritating. Like I said, probably it's fine under your specific circumstances, but it's good practice to not assume your circumstances to be the One True Circumstance. That's all. :)