Well look into the "theLevelInfo" in the scene inspector, in that you will find a value called "nearClip" which is set to 0.1 (10cm), this is the distance the clipping happens and if your camera gets closer you view through the surfaces.
You can try changing the value of nearClip to fix that, but the nearClip value is already set to a quite ideal value, so you are left with the alternative of preventing the camera getting too close, like with playing with the camera distance values, but that is not going to the root of the problem.
The ideal solution would probably to have some kind of collision box for the camera of 10 or maybe better 20cm so the clipping will never happen, I think the current camera is just a point.
If you are a pro you can also try to change the clipping algorithms in the source code, it needs a fix anyway, since it is slightly different in openGL and directX at least it was like that a while ago, I could not remember if we fixed that.