Where Peter is, there is the Church. And where the Church, no death is there, but life eternal."
St. Ambrose of Milan, "Commentary on Twelve Psalms of David" c. 389 A.D.
Over the centuries, some of those in disagreement with the magisterium set up their own 'independent' churches but retained the word 'catholic'. Independent Catholic Churches. These are not in unity with the Holy See. So, excuse me but I still don't understand your comment: There are no catholic groups independent of the Vatican.
These people can call themselves whatever they want, if it makes them happy. I can call myself President of the United States, but that doesn’t mean Marines are going to salute me. As far as these churches go, I have more respect for Luther and Calvin.