He spent weeks trying to get help from them, to no avail. It's more than reasonable for him to post a negative review at this point, explaining the situation, taking blame where he should, and warning others to think twice.
All I want to see from the CEO in a situation like this is: "I'm sorry. We fucked up. Here's how we'll make it right, and here's how we'll make sure it doesn't happen again."
And if you genuinely can't say that because you don't think the customer is right and you're not willing to do anything for them, just keep your mouth shut.