You're missing the key takeaway. The issue is not that you misread a comment. The issue is that your reply is non-substantive, and that you would have picked up on that, had you entered the discussion with a healthy, productive attitude, rather than the attitude you apparently came in with, of "how can I show myself to have superior knowledge?"
Let's say you hadn't misread the comment (i.e. it was as you originally perceived). Would your reply be helpful then? No. The parent was obviously suggesting that managers face workplace abuses that could be remedied by unionization. Even if they had said "join the union" -- as you leaped at the chance to correct -- was your comment substantively replying to this (actual) point?
No, it wasn't. Whatever the structure of unions-as-they-exist, the proposed solution most assuredly does not involve "join a union that prohibits you". So the existence of unions that prohibit managers isn't relevant. At most, if you really needed to show off your knowledge, you could have said something like:
"That might help -- but, nitpick, it would probably have to be a separate union from 'the' one representing warehouse workers, as there are reasons that US unions separate out representation by role. <insert historic and legal context>."
But then, phrasing your objection appropriately like that makes its value to the conversation seem even more dubious. Whether or not unions prevent this kind of manager abuse is irrelevant to the implementation details of how those managers unionize.
>I feel like you're kinda throwing stones in a glass house
No, the situations aren't the same. You recognize your comment would be irrelevant had you correctly read the comment you were replying to. But even if I had read your full comment, my reply would still be relevant, as a guideline for how to notice when you might have misread someone, and how to ensure that you're substantively replying to a charitable reading of someone's remarks. That advice is still relevant, and still serves as a useful takeaway.