Nope, it ain't so. Titanium might be really strong in tensile and bending strength, but it's not hard to cut. Doc just turned some in his lathe, eh? The same cutting tools that handle gold, platinum, and stainless steel jewelry will cut a titanium ring.
There actually is a problem with cutting titanium rings off a finger. The high strength of the ring means it can't be bent to allow it to be removed like a gold ring. Instead, the ER tech will have to make two cuts, one on each side of the ring so it splits into two half-circle pieces.
Snopes says this urban myth comes from jewelry shops who would rather sell the much more expensive, and therefore profitable, gold, silver, and platinum rings. These metals are easily worked, therefore the shops can custom-make settings. Titanium, not so much.
Myself, I wear a tungsten carbide ring. It was really cheap at wholesale, it stays shiny, unlike tungsten, and removing it in an emergency situation only requires the simple application of vise-grip pliers to crack and break it.