[montanalow]

The article goes on to mention Pepsi & Coca-Cola's more rigorous experiments, with a similar finding of no value.

You're essentially asking for proof of a negative, i.e. prove that social media does not matter. This is as you stated impossible. This is also why the burden of proof is always on the person making the claim.

If companies are going to spend money on something, there should be proof that it has value.