I doubt this would work for most people these days. Especially with a recent WT saying you can't claim your baptism was invalid. Maybe it was a loophole they recently clamped down on.
But I don't doubt the story, or that people successfully annulled baptisms in the past. We too often think of JWs as uniform and monolithic. Which admittedly they are to some degree, and by comparison with other groups. But there is also variety of practice among JWs. Sometimes it comes down to personalities. If your local elders like you and your family are well liked you can expect different treatment than someone the elders don't care for. There are egos, ambitions, grudges, guilt and all sorts going on in elders' behaviour too.
Plus we also tend to accept the JW notion that the WT has a fixed teaching on most things. In fact there are so many statements in the WT on most subjects that in many cases you can pick and choose and emphasize a liberal or a hardline position as you wish for the circumstance. JW elders do this all the time without acknowledging it. They pretend that WT statements are clear cut or they are following the latest instructions. It's rarely as black and white as that. Like any complex rule system elders can manipulate the ambiguities to get the outdone they want, even if they don't acknowledge or even realise that's what they are doing.