Fertility or lack of it is something that can't be ignored when considering whether a foundling is correctly identified.
In the case of Souvenir de Pierre Notting, there is information from the breeder that suggests it would be very difficult to pollinate.
The July 1899 Journal des Roses reference recently added to HMF - authored by Soupert and Notting before the rose was released - refers to a rose with blooms that last a long time - an unusually long time for a Tea. It describes the way the outer petals dry off while the bloom keeps renewing itself from the centre:
"the outer petals do not fall off, they dry up, the center petals grow and renew the flower like this until all the petals have reached their greatest development, then the flower immediately falls off entirely.
Sometimes there are no pistils or stamens in the center, but tiny petals which develop slowly and are thus the cause of the long duration of the flowers."

I have searched plants for hips or unusual blooms with fewer petals and visible reproductive bits and have not found any to date but given that account, which is a very accurate description of the rose we grow under that name, it seems that any natural pollination would be very difficult and naturally occurring hips unlikely.
Perhaps a determined breeder might have assisted - the longevity of the bloom alone would have been a sought-after quality.
All four roses that have Souvenir de Pierre Notting listed as seed parent come with a stated pollen parent, so presumably deliberate crosses/ assisted reproduction.