The NMR relaxation data on Sr 2 CuO 3 [Phys. Rev. Lett. 76, 4612 (1996)] are reexamined and compared with the analytic theory of the dynamic susceptibility in the S= 1/2 antiferromagnetic Heisenberg chain including multiplicative logarithmic corrections [Phys. Rev. Lett. 78, 539 (1997)]. Comparisons of the spin-lattice and the Gaussian spin-echo decay rates (1/T 1 and 1/T 2 G) and their ratio all show good quantitative agreement. Our results demonstrate the importance of the logarithmic corrections in the analysis of experimental data for quasi-one-dimensional systems and indicate that the dynamics of Sr 2 CuO 3 is well described by an S= 1/2 one-dimensional Heisenberg model with a nearest-neighbor exchange.