Incidentally, there has been some recent publication indicating that this may not be true, albeit for different reasons than the typical Radium Girls pathology:

https://www.northampton.ac.uk/news/wwii-military-watches-pot...

I don't think this is true. Army training taught that if the glass over radium glowing dials in a vehicle was compromised, to cover it with wood or cardboard (if that is all you had) and tape/secure it down.

A squad leader of my Army platoon once had a crate of about 30 compasses that had radium markings. Anyway, he had the box in his truck, left the gate at Fort Benning then when he returned later, he set off the radiation detectors at the entry gate. Caused a full base lockdown and needless to say, he didn’t have a very pleasant time until they figured out that the compasses set off the detectors. This was in 2004 when we were on a high alert for dirty bombs.

That sounds like protection against alpha/beta radiation as well as abrasion.

Radium was also used in chocolate, drinking water, toothpaste, cosmetics, suppositories, jock straps and "radioactive “bougies” – wax rods inserted into the urethra".

Possibly, but the issue is with the workers applying the paint.