I have to agree. The lower end of the 95% confidence interval on the hazard ratio is 1.01, which means this result is just barely significant at a p-value of 0.

I have to agree. The lower end of the 95% confidence interval on the hazard ratio is 1.01, which means this result is just barely significant at a p-value of 0.05. (The null hypothesis is a hazard ratio of 1.) After any kind of multiple testing correction, this result is not significant.