Yes.
Most of the accidents from these aircaft are caused by them doing things they were not designed to do by pilots who are not familiar with them. That hapens at low levl at shows, not poddling along over the countryside.
These are not 'old aircraft' - they are aircraft whose structural integrity and general condition is way in excess of the standards that were in use at the time they were built.
They are rebuilt and refirbished to exceptional standards by very highly skilled people to very stringent guidelines.