You are after all partly right; its relatively easy to make an expanding or semi-expanding projectile out of a Full Metal Jacket rifle projectile. If a proejctile has a lead core, you can expose this and in theory make an expanding projectile.
International conventions outlaw the use of expanding projectiles for war and stipulate Full Metal Jacket or non-expanding projectiles.
Whilst you cant use them for war, they are not prohibited as expanding projectiles are used for deer hunting purposes for example. In fact, this is stipulated by hunting laws in many Western countries, as they are very efficient and you cant use non-expanding projectiles on deer-sized or larger animals.
How ever, I clearly did not express myself clearly; the term 'Dum-dum' is merely not the correct term, as this was an Arsenal in the 1850s in India, that was the gist of my comment and sorry, that I didnt convey this clearly.
On the main themes we agree. The terminology is after all just a matter of (me) splitting hairs.
The term is wrong albeit in widespread use, as is the term 'shrapnel' for fragments. Both are wrong and both bug me, but thats just me