Yes, I understand that, at least at a high level. I’m making a narrow point that the article didn’t teach us this and it actually was essential to understanding the claim. Quoting the article again:

I won’t go into the M/M/1 part, as it doesn’t really end up affecting the Important Thing I’m telling you about. What does matter, however, is that ‘∞’.

This turned out to be wrong. It does end up affecting the Important Thing and the discussion was severely incomplete without it.