Is it true a tungsten ring is so strong, it can't be cut.

No, it is not true. Tungsten rings can be cut off. They can also break, shatter or crack. Tungsten rings are so strong that there is no give to them, so if they are to break, they almost shatter due to the stress. It is almost like glass, they dont just chip, and they usually shatter completely. Of course, there are different degrees of how things break and that will correspond to the damage that is done to a ring. Just note that tungsten rings can be cut and if are ever in an emergency and need to have your tungsten ring be removed, you will be just fine, it can be done.