When you stream videos it uses another block inside the video card, different from the case when you display a 2D image (desktop) or a 3D application - playing games.
It's a hardware video decoding block (
UVD 3 in your HD7950) and got damaged at some point (probably by overheating the card while gaming in OC mode). Skype only recently started to support this hardware feature.
I had a few AMD cards (including a HD7950 GHz edition) and they where running hot even without overclocking.
The main clock is not related to this ASIC block, so any modification of the GPU clock will not affect it.