NavMesh Agent breaks Parenting?

Forgive possible double post. I posted a very similar question in Animation, but further testing suggest it is a navigation issue.

Using Unity 5.1 Personal

All of my games action takes place on a "table" that the player can rotate by clicking objects.
I have mechanim animated character that walks around on the table.
The characters is a CHILD of the rotating table.
I can use basic Animator control with my own script and the character rotates with the parent table correctly.
However, WHEN I add a nav mesh agent to the character to enable him to wonder about the table.
Rotating the table results in the character not rotating and moving eradicatly.
What am I missing?

FYI: I have many other objects on the map that rotate just fine, including cars that drive on roads that move etc.. I did nothing special for that to work other than parent everything to the table.

 

OK, the problem seems to be that rotating the table does not rotate the navmesh. In fact it seems that such a thing is not possible with a navmesh. Unless I am mistaken, I cannot use navmesh based navigation for my rotating table.. thoughts?

 

Can you have a invisible nav-agent on a static navmesh, and transform the position to a visible character on the rotating table?