The problem is with bStatic. It does exist, but it's not been mad evisible in the editor, as you can see from this comment in the source code:
Fortunately for you, I wanted to attach some static meshes to a mover a while ago, so I have a solution already:
var const bool bStatic; // Does not move or change over time. Don't let L.D.s change this - screws up net play
You need to make a new class in the editor. Right-click on 'Actor' in the actor browser and then 'new'. Call it whatever you like and put it in the 'MyLevel' package so it is embeded in the map. In the window that opens, click on 'Tools->Compile changed'. The new class should now be visible in the actor browser. Right-click on it and open its properties. You will want to change the following:
You should also put a StaticMesh in the 'StaticMesh' field, otherwise it will be invisible when you place it. You may also want to change the collision if you expect players to touch it:
You may also need to set 'bHardAttach=True' for it to attach properly to the mover.
There is a simpler way too: Place the static mesh as a mover instead of a normal static mesh. Movers can be atatched to other movers perfectly alright (see BR-Skyline blimp for an example). My experiments showed that using a mover results in lower fps, but you may have to do it that way if the comment about 'scewing up net play' is really serious.