Does THIS TEARDOWN help?
This Video may also assist
Have a look at THIS pic - under the guys finger you can see half of it.. It appears the brass washer sits in the circular dent in metal base plate.
The SOURCE ARTICLE - step 6
It appears the base is a little different in this article compared to the iFixit teardown- clear instead of black plastic insert in base.
This is by my own intuition and that I disclaim any damages you might incur during following of the propose solution, but if you got guts and some guts and a few more guts to do this then see below;
I don't have any screen shots but hopefully I would be clear enough, if you want me to explain it to you personally I would be glad to attend to your concerns mail me at polo_escape@yah
So let's # the rings so we won't get lost, and I would be referring to it as #'s
1->small brass ring
If you were to examine the kinect, you would notice that there is an opening along the base, assuming you have already removed the plastic cover and your on the metal plate with 4 #0 screws, one is an opening for the wire that connects to xbox and the other one is for a side which exposes a gear.
Examining further, you would notice Hexagonal Screw head which underneath or on the other side is a female nut (meaning a bar is to go through), so with the data we have already collected it is enough or almost safe to say that the rings are to be placed on top of the exposed gear so it should be like these;
a little visual;
So using a screw to help you keep holding the rings in place, you can place back the gears and the plate without any trouble.
There is a caveat though, never ever let go of the plates from being held down while placing everything in place, if you do, I think you're done, also work in a place where there is good lighting and minimal to none crevices so just in case you've accidentally release the rings from being held, you'd still be able to find it.
That's it. Many Thanks!