Flowplayer settings not appearing, even after adding flowplayer files

I followed the installation notes to the letter and attempted to install flowplayer:

* I enabled the SWF Tools module (6.2.5)
* (I also enabled SWFObject, SWFObject 2 and 1 Pixel Out. These all seem to be working fine.)
* I downloaded the Flowplayer and Flowplayer 3 files and put them in the correct places
* Flowplayer is sitting happily at modules/swftools/shared/flowplayer/FlowPlayerClassic.swf
* Flowplayer 3 is modules/swftools/shared/flowplayer3/flowplayer-3.1.5.swf

However, I was stuck with the next step:

"You also need to tell the FlowPlayer 3 module what the player name is, as this changes with each FlowPlayer release. You enter this at Administer > Site configuration > SWF Tools > FlowPlayer 3, and it's under the File section."

This page doesn't exist for me. If I go to Administer > Site configuration > SWF Tools, I see items for embedding settings, file handling, generic players, 1 Pixel Out (again, working fine), and CCK formatters. Nothing about Flowplayer.

In the file handling section, Flowplayer isn't showing up anywhere. The status page (in Administer > Reports) doesn't list Flowplayer anywhere either.

It seems odd, because 1 Pixel Out, which is a similar third-party item, is working just fine. But I did think it was strange that 1 Pixel Out has its own SWF Tools sub-module (which I enabled), but Flowplayer does not. As far as I can tell from the installation instructions, SWF Tools is supposed to just detect when Flowplayer is there based on whether the files are present. I've put the files there, but nothing seems to be happening. What am I doing wrong?