I'd agree with you if it was just one person who messed up. But shit flows downhill. Imagine if the web publisher's time was wasted with constant re-work leading to delays of other important tasks because EIGHT people whose jobs involved vetting the materials couldn't be bothered to get their acts together. The web publisher's going to be on the hook for not getting things done in a timely manner even though none of it was a result of her actions. It's perfectly legit to ask them to get their acts together, particularly if this is a chronic occurance.
Yep, eight people screwed up and deserve the blame -- I'm not saying they aren't blameless. But it's likely going to keep happening again and again. It's happening right now in thousands of organizations or groups across the country even with redundancies in place.
You can focus on blaming and shitting on the screw ups (what some are doing), or you can try to design a process to minimize errors but allows for corrections to be made if/when they're discovered (what the OP's "work situation" was about). Since the OP has stated that the web editor has since made the corrections, it appears that they're going with the latter approach.
In this case, let's put it into perspective... Publishers with professional proofreaders, decades of experience, and veteran editors let typos happen on 100,000 copy print runs. Doesn't sound like OP has the same level of organization dedicated to publications.