Its not the support of the box, so much as its the box itself. You are only hanging that fan on about two threads, three at the most, if those are regular electrical boxes.
You're definitely right... my other post was a bit half hearted, and I should have been more specific.
Here's the more complete story: my 1950's house has ceiling boxes with very weak metal braces. The $30 Lowe's fan above our bed was vibrating and swinging like crazy, obviously stressing it a great deal. I just didn't trust it to hold a fan above our heads while we slept. Isn't it an ugly little brace? I especially didn't like it being secured by two rusty nails in the BOTTOM of the joist. (Surely attaching a brace that nails to the sides of the joists would have been more robust for a vertical load???)
What I did was remove the whole thing, run a 2x4 above the electrical box, and screw a new electrical box into it... BUT, I also secured the fan "bracket thingie" directly to the lumber with very long screws that run through the box. (The fan came with them because this was the suggested way to install it.)
It goes without saying that even though my initial plan was just to strengthen the box, once I had done all the work I couldn't resist putting a nice new fan in.

After all, who would want to reinstall a crusty old fan that was almost certainly worth less than the brand new electrical box above it?