Try a private message before a public callout. Most people fix things faster when there’s no crowd watching.

An audience changes what a correction is for. Once other people are watching, the person you are correcting has to protect their standing before they can even hear you, so they defend instead of fix. Privately, there is nothing to lose by agreeing with you.

Before you post the reply everyone can see, try the one only they can. Say the same thing, minus the witnesses. If it still needs saying publicly afterwards, you will know, and you will have been fair about it.