As we have discussed here before, several of the rambler roses in Europe that were bred in the USA are incorrectly labeled in European gardens and in some cases have been distributed under the incorrect name.

With respect to DP there are a couple of distinct characteristics that can help identify it. New foliage is frequently "bronze" colored with the new leaves showing a definite coloration that eventually turns green. Another characteristic is pedicels that are almost free of the tiny hairs that are a characteristic of ramblers that have 'Turner's Crimson Rambler' in their genetics. Many of the Walsh roses have a profusion of tiny hairs on the pedicels that identify them as "not DP."

We are in the midst of a huge rain storm now so it isn't practical to take any photos today, but I have a photo, https://www.helpmefind.com/rose/l.php?l=21.267841, under DP that should give you a good idea of the flower and pedicel. I have also uploaded another photo of the flowers which I think adds verisimilitude to your statement that the flowers are not flat when fully open.

Followup 10 days later: The rain has stopped and there is plenty of new growth on 'Dorothy Perkins'. So here is an illustration of the new growth that I termed above as "bronze."