That’s an excellent question and I’m glad you brought that up! LOL
According to what I could find, the St. Bartholmew skinned alive was not the same one in the painting (the original Bartholomew). There was a St. Bartholmew (named after the apostle) who was said to have brought Christianity to Armenia. It was this Bartholmew who was “flayed” (skinned alive) and crucified upside down in the 8th century.
That doesn't work very well either. Armenia declared Christianity the state religion in 301, the first nation to do so.