In the late 80's when I first started archery there was a big issue with Beman arrows. They didn't exactly explode like the stories we've all heard, but they did splinter really badly, especially on contact with a new straw boss that was still hard in most places or if you missed the boss and hit the target leg etc. I have personally seen this on many occasions during the late 80's, I believe Beman received a lot of complaints at the time and decided to research other manufacturing techniques. Can't remember the name of the Beman arrows, but I'm sure it was before the Diva and DivaS arrows.
I believe the reason for the ban on all carbon arrows at some clubs with shared grounds, is not due to them being difficult to find, but due to the fact that carbon splinters are difficult to remove from fingers/hands etc, we were told years ago that carbon splinters are potentially poisonous and could cause other medical issues for the archer (whether this is actually true, I don't know). I remember the story of an archer who overdrew an all carbon arrow and the arrow hit the riser and exploded and buried hundreds of pieces of carbon into his hand resulting in horrific injuries, apparently all the pieces couldn't be removed even with surgery. I can't remember all the details, but I believe the person was never able to shoot again.
I'm talking about things from over 30 yrs ago and going by what I can remember and was told at the time, so please forgive any inaccuracies.