Well, it's impossible to prove that there is absolutely no effect.
That's one of the big confusions of science - it's impossible to prove absolutely that ANYTHING has absolutely no effect. One can only put limits on that effect, say for example, that adding substance z to a chicks diet makes less than a 0.01% difference in weight at age 10 weeks - you can never prove that the effect is 0.
So when scientists say "evidence does not suggest that a causes b" that's exactly what they mean. They are NOT saying conclusively "a does not cause b, ever". it all comes down to statistics and probabilities, which are phenomenally useful - they provide those shades of gray that leave questions open. E.g. if something is demonstrated with p=0.1, that means there's a 10% chance that the effect noted was simply by chance. If p=0.0001, there's only 1/100th of 1 % likelihood that the effect occurred by chance, and it's reasonably to conclude that the effect was real.
It generally comes down to sample size - an effect that looks quite large, for example 4 females in a hatch of 5 chicks, or 80% - will have a high p value, suggesting that it's just chance. However the same sex ratio in a large sample - say 80,000 females out of 100,000 chicks, is likely to have a pretty low p, saying that gender ratio almost certainly differs from 1:1.