Nothing has been proven.
Science is the discipline of publicly testing ideas by systematic observation, controlled experiment and Bayesian inference. As such, proof is simply not relevant to what it does, which is produce knowledge. Knowledge--unlike faith--is inherently uncertain.
It'll take a few hundred years for the popular science press to catch up to this. What is being presented here is evidence that the idea p-p fusion powers the sun is correct, so the posterior pluasibility of that idea goes up, although not to 1 (which would be a certainty, and therefore an error: an idea that was immune to additional evidence.)
If neutrinos had not been detected, the plausibility would have gone down, although not to 0 because that would be the same error. Science never disproves anything any more than it proves anything. Proof and certainty are like the philosopher's stone sought by alchemists: a fundamentally mistaken goal.
Philosophers are the alchemists of epistemology, discovering all kinds of cool things while on a hiding to no-where.