It also goes the other way - the update to the directory can be fsynced but the file lost. This can break the "create temp file, write, close, rename to current" scenario (when the intention is to replace file contents atomically).
POSIX doesn't guarantee the order in which data hits the disk, so the above scenario can become "create temp file, write [contents still in memory only], rename to current [written to disk], power failure".
I believe there was a bug where this scenario had worked for a long time then one filesystem (ext4?) pushed closer to what is admissible under POSIX (non-obvious reorders of physical writes) and people started getting random data corruption in programs which used write & rename.