This is not true. This depends on how the file was opened. You may request DIRECT | SYNC when opening and the writes are acknowledged when they are actually written. This is obviously a lot slower than writing to cache, but this is the way for "simple" user-space applications to implement their own cache.

In the world of today, you are very rarely writing to something that's not network attached, and depending on your appliance, the meaning of acknowledgement from write() differs. Sometimes it's even configurable. This is why databases also offer various modes of synchronization -- you need to know how your appliance works and configure the database accordingly.