You're not wrong. In fact, the sentiment that you brought up about other people's unhappiness being a lack of their own stoicism is touched upon (I don't think he says it quite like that) by Aurelius in his writings, but again, that doesn't stop him from trying to be a good person. I have not yet gotten to read much of other stoic's works (after all, this whole thread came about because I tried but got my book stolen by my husband) so I can't say much for their takes yet. Overall I have found a lot of helpful concepts in what I have read of stoicism, but that can also be said for Buddhist teachings and other philosophies/religions but I guess what we are both getting at here is that none of them are perfect.
To be fair, my answer was more of an attempt at an obvious lawyerly cop-out than a genuine refutation of what you said. Nonetheless, I do think it ultimately depends in how it's applied by the person.