Perforation pins do not cause white perf tips but separating the stamps will cause a bit of natural gum loss that shows up more when the gum is not white. The older the multiple when broken the more likely gum loss is. Gum ages and can dry out. I would not expect to see the white areas on the tips in most cases if a stamp was regummed unless somebody was a pro and took a lot of time and care to sand them as Don stated. In the case of the original OP's magnified image it was obviously not sanded because the perf tip fibers are still intact. If regummed, the tips might be covered in the new or redistributed gum which is why it would be sanded in the first place. If gum collects on the tip fibers from applying gum it is a tell for regumming and you would want to get rid of it.
Personally I think that both of Wert's examples are regummed. I see gum on the inside perf hole edges on both. Could be wrong given that the pics are a bit unclear.
PS: Magnification can be a good thing but like drinking alcohol it can become a problem if taken to far. The forest for the trees and all of that.