No, it does not. He falls prey to conformational bias.
First the difference in number of flights (135 vs 120) is insignificant. Second, first Souyz flew in 1966 (or 1967, don't remember). It did that almost 15 years before the first shuttle flight. Therefore it had to use older technology and do so without much of the experience, technology and knowledge that the designers of the shuttle had. Perhaps it is not coincidence that the 2 losses Souyz had were before the shuttle even took off. Compare this to the shuttle failures.
I think that Souyz is more reliable than the shuttle, but I admit that this is opinion rather than data supported hypothesis since data points are few and unreliable (near misses).