Camera rendering things it shouldn't

I have a main camera which is supposed to not render all GameObjects in the layer "Icons".

I have two GameObjects presently in the layer Icons. (this is run-time, by the way, so I know it's not changing between the time I set them and the time I render them)

The camera has a culling mask that definitively is supposed to mask out the layer "Icons". In other words, under Culling Mask, the layer "Icons" is unchecked. However, the GameObjects are being rendered! In fact, if I set the culling mask to be "None", the only things that are rendered are these GameObjects (and the Skybox). This is really confusing!

To test, I have another layer called "Player" which has the player in it. I removed the "Player" layer from the culling mask of the camera. This worked properly: the player was no longer rendered. Then, I moved the player to the "Icons" layer and kept the "Icons" layer out of the culling mask. The player remained visible!

I'm kind of at the end of my wits here. I've tried moving the Icons layer to a different layer number, but that didn't work.

Does anyone have any ideas as to what the problem might be?