I used this test to compare the survival distribution for 2 cohorts and my p-value result is 0.2, does this mean that there is not enough evidence to reject the null hypothesis: the survival distributions are equal and that it means that the survival distributions are indeed different?

From this link, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC403858/ it seems to suggest that the log-rank test can be a poor indicator if there are overlaps between the survival curves. is that correct?