Did they really prove there was 'no association' or did they just fail to reject the null hypothesis that there is no association? These are diabolically different things!
Indeed they are, but according to the null hypothesis precept, without persuasive contradicting evidence, there is no association. The burden is on experimental evidence to contradict that assumption, and if positive evidence isn't present, then the default assumption is correct. Think about what proving no association actually means. That would require proof of a negative, which is a widely recognized logical error,…
What you have said above is horribly wrong and is exactly the point I am making. If it is true then I can prove anything I like just by designing a bad enough experiment.
For example, suppose I want to prove that the moon is made of green cheese. I can start with a null hypothesis that it IS made of green cheese. Then I can point my telescope in the wrong direction and find no evidence that it is not made of green cheese. Using your logic I am free to then conclude that my null hypothesis is true.
You cannot just make any null hypothesis you want and then when you fail to prove it untrue, claim it is true. If you want to make a positive claim about the null hypothesis (for example, claim there is no association between salt and blood pressure) then you have to test it directly with positive evidence in its own right.