I assume you are referring to
" If the seven associations that did not reach P ≤ 5 × 10−8 when additional data were considered are assumed to have been false-positives, the false-discovery rate for borderline associations is estimated to be 27% [95% confidence interval (CI) 12–48%]. For five associations, the current P-value is > 10−6 [corresponding false-discovery rate 19% (95% CI 7–39%)]."
That doesn't show anything relevant. Failure to replicate at 10-8 is a ludicrous way to define non-replication; to paraphrase Cohen, surely God loves the 10-7.99 almost as much as the 10-8... This paper needs to adjust for power, and ask how many hits one would expect to not replicate at 10-8 given the power of the replicating studies. If you do remember power, GWASes replicate fantastically, for example https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3681663/
"Replicability rates are high within Europeans, with 155 successful out of 181 attempts (85.6%), when only 9 positive replications (∼5%) would be expected under the null hypothesis of no association (binomial test, P<10−16). This excess was robust to the significance threshold (e.g. 122 observed vs. 0.18 expected if only replication attempts achieving P<0.001 are considered successful and 56 observed vs. 1.8×10−5 expected for a threshold of P<10−7, Table S5). Moreover, replicability rates within Europeans approach 100% when accounting for statistical power. For the 168 attempts for which we could calculate the power to replicate the original finding (Table S5), we observed 147 positive replications, which is almost identical to the expectation of 149.1 positive replications given that average power is 89.1% (see Materials and Methods). This is expected, since most GWAS already contain an internal replication phase [1], [24]."
> and, believe me, many GWA studies have been published with much less significant p-values
I don't think they have. Ever since Ioannidis and others demonstrated what a total debacle the early candidate-gene studies were around 2009-2011, using the first GWASes to demonstrate that, GWASes have been pretty standardly done at 10-8.