Here's another solution I found: download a different camera app. There are some apps that advertise no shutter sound (just search "silent camera shutter" in Google Play). I've just tried a few free ones. Two apps both called "Silent Camera" do take pictures with no shutter sounds, as does "Camera ICS" (you have to turn on silent mode in the settings). "Camera ICS" seems to have the most features of the three, and it has a pay version that removes ads. I'm not sure about features like burst mode, like secretmethod70 uses, though I found "Camera ZOOM FX" which advertises burst mode. I haven't tried it because it's pay, though it's currently on sale for $1.49. It also says about its silent mode: "only if your device supports it," but "Camera ICS" said the same thing about its silent mode, so it seems promising.
UPDATE: "Camera ZOOM FX" silent mode doesn't work. It offers the workarounds of either root your phone, or use burst mode, which gives lower resolution pics. I'm assuming that the burst mode just uses the video camera, so that's why it will be silent.
UPDATE 2: I just bought "Camera ICS+" ($0.99) and can confirm the silent mode works, just like the free version. Ads are removed and a few extra features are added, like burst mode and time lapse. One thing I don't like is that it doesn't display full screen. The bottom 1/4 of the screen is taken up by the shutter button section. Also, the photos at 8 MP are not 16:9, like in the stock camera. You have to change the resolution to 6 MP to get 16:9 pictures. I suppose this might be more accurate in terms of the actual pixel resolution, bu the stock camera at least lets you chose the aspect ratio independent of the resolution. Also, if you choose 6 MP (or other 16:9 resolutions), it adds black bars to the upper 3/4 part of the screen, so your view of what you're taking a picture of seems even smaller. I wish it had a full screen view for taking pictures, but otherwise it seems like one of the better options for silent picture taking.