I seem to recall saying not to do that. Often in this kind of situation restarting SQL makes the problem way worse.

The message you posted said 'inaccessible files or insufficient memory or disk space.'. It usually is actually inaccessible files. Lack of disk space alone will NOT make a database unavailable. It just makes it read only and makes data modifications throw errors.

I suspect what happened here was that the disk became full and something in the IO subsystem temporarily made the disk unavailable as a result. If SQL notices that a disk is not available, it will throw errors and it will not retry to see if that disk has come back until either SQL is restarted or the database is taken offline and brought online. Hence why the restart worked in this particular case and why you could see the disk at a slightly later point, SQL had already tried and failed and wouldn't retry.

I must emphasis, restarting SQL when you have error 945 is a dangerous thing to do and can make the situation worse. Hence it should not be done without guidance.