So.. I decided to add some weighted meshes elements to existing model (the existing part seems to be important because this problem did not pop up in other model that I created from scratch):
My project has a skeleton with body parts. It has 3 changable skins. I decided to make head (which is part of the skin) a mesh and add couple of bones so I can do mesh deform. So I "mesh-erize" the head images in each of the three skins. So far so good.
Bind the two bones to each mesh. So far so good
The animations always seem to be working..in 2 of the skins. Everything deforms nicely and then I switch to the third skin and bone movements have no impact. If (in animation mde) I try to edit with the "problem skin" selected, one of the bones does not seem to be attached to anything (moving it around does not impact mesh at all), while the other acts as if it was "main bone", meaning, moving it, moves the whole mesh without any deformation. Looking with the pies look - in the third skin - one bone impacts all the vertices 100% while the other 0%.
I have a nagging suspicion that the problematic skin will always be the one that was selected in the edit mode when the two bones were added. It somehow messes up the auto calculation when the weights are calculated.
Or perhaps it's not a bug and instead I'm just missing something super obvious.