This is nothing the HP developers, deliberately or not, broke. This is something they decided.
Digital camera sensors always require a tradeoff between image noise and the time required to take that image. You can get a picture with half the noise, but that also comes at the price of half the update rate. This is most apparant in low-light conditions with low-end cameras such as the TouchPad's.
The noise in the image is always there, it's a characteristic of the camera sensor. Simply said, if the camera gets less time to take in light the resulting image is dark and has to be amplified to be usable. And with that amplification the noise also gets amplified. That's what you see right now.
P.S.: I cannot confirm the OP's observations, in the video the image quality is pretty much the same as in still photos. In videos, however, the noise gets smoothed considerably as a side effect of the video compression.
It is arguable whether the decision to sacrifice image quality for a better update rate was a good one, but it is certainly not a bug, it is a deliberate decision. That being said, they could have left that decision to the user by means of a setting.