Doesn't uranium mostly emit alpha particles? They won't escape the bottle. It's in the body when the harm can occur.

I have worked in La Hague. It was common knowledge that during an annual check of staff, the tests were accurate enough to identify smokers and it was always asked if the subject was a heavy drinker of San Pellegrino because this had an impact of measures. Ingested radioactive material is far more dangerous than exposition to radiations. I am mostly pro nuclear, but IMHO, the recomandation to avoid San Pellegrino for young childs should be taken seriously.