Based on my research of the matplotlib codebase and the bug description, I can provide the fix. The issue is in the `Axes3D.draw()` method in `lib/mpl_toolkits/mplot3d/axes3d.py` which does not check the visibility flag before drawing.

Looking at matplotlib's codebase, the `Axes3D.draw()` method needs to check `self.get_visible()` early and return without drawing if the axes is not visible.

Here's the patch:

--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -41,6 +41,8 @@ class Axes3D(Axes):
     @artist.allow_rasterization
     def draw(self, renderer):
         # draw the background patch
+        if not self.get_visible():
+            return
         self.patch.draw(renderer)
         self._frameon = False