To me, the theory seems incoherent. Why would radiosondes contain a radioactive gas in the balloon? The purpose of the balloon is to lift the whole sonde (measuring equipment) into the air. Usually a light, harmless gas like hydrogen is used.
There is no reason to use a radioactive gas. Moreover, if there was a radioactive gas, there is absolutely no way that civilians would be given these devices to test or deploy.
Now the other part of the theory is that they show signs of organophosphate poisoning. This is, while far from proven, an interesting idea. But I think there is no way this could have been a result of burst balloons or anything like that.