GWAS studies typically use a p-value cutoff of 5*10^-8 to avoid exactly that problem.
as a matter of fact artificially raising the cutoff to make the results sound more convincing is a form a p-hacking
it is exactly the opposite of how p-values work. a smaller p-value does not make a result more reliable, it makes no sense whatsoever to reject a 10^-7 but trust in 10^-8
the misuse of p-values in the world is rampant - the only people that don't misuse them are those that do not use them ;-)
"The most commonly accepted threshold is p < 5 × 10−8, which is based on performing a Bonferroni correction for all the independent common SNPs across the human genome"
Any what do you mean by "opposite of how p-values work"?
Obviously if P(data or more extreme|null hypothesis) = 10^-8 it's significantly less likely to see the data if the null hypothesis was true, than if P(data or more extreme| null hypothesis) = 10^-7.