Nope, you're thinking of regression coefficients, where you'd be correct that usually the null hypothesis is $\beta = 0$. In this case, what's being reported are odds ratios, so the null hypothesis would be that OR = 1.
The parent comment's point is that although the reported effect is significant at $\alpha = 0.05$ (the usual "95% CI" you mentioned), there are other problems that render their test of this hypothesis less than valid.
The parent comment's point is that although the reported effect is significant at $\alpha = 0.05$ (the usual "95% CI" you mentioned), there are other problems that render their test of this hypothesis less than valid.