Or were the discoveries independent?

I'm not sure. If they were connected, it was probably by way of the grapevine via the Schmidhuber/Hutter labs.

SI let a huge, track-record-building accomplishment slip through its hands

Meh, people wouldn't have called it huge, and it isn't, particularly. It would have signaled some positive things, but not much.

So if I read correctly, someone at SI (Eliezer, even) had an original insight into cutting-edge AGI research, one strong enough to be accepted by other cutting-edge AGI researchers, and instead of publishing a proof of it, which was trivial, simply gave it away and some students finally proved it?

Surely Hutter was aware of this issue back in 2003:

Another problem connected, but possibly not limited to embodied agents, especially if they are rewarded by humans, is the following: Sufficiently intelligent agents may increase their rewards by psychologically manipulating their human “teachers”, or by threatening them. This is a general sociological problem which successful AI will cause, which has nothing specifically to do with AIXI. Every intelligence superior to humans is capable of manipulating the latter.

• http://www.hutter1.net/ai/aixigentle.pdf