The story is like your first scenario. We call this process "attribution."

In the 1970's, one hundred and twenty years after Monsieur Vibert introduced 'Joasine Hanet,' 'Joasine Hanet' was no where to be found in commerce. Plants lose their labels and thus their identities easily, especially when major catastrophes or world event intervene. But in three favored locations where roses can live a very long time without much care, three identical roses were found, with no labels and no history. Through study of roses of its type, its foliage, its habit, and its color, careful rosarians decided that 'Joasine Hanet' is the mostly likely identity of the rose found in Southern California (given the study name "The Portland From Glendora"), the rose found hundreds of miles away in Northern California (given the study name "Aunt Sally") and the rose found across the ocean in Australia (given the study name "Kew Cemetery Portland").

The story can go full circle if a respected botanical garden produces its own, independently grown and labeled specimen of 'Joasine Hanet.' When that plant is compared to "The Portland From Glendora," "Aunt Sally," or the "Kew Cemetery Portland," we will know the attribution is correct.

Careful botanical collections always note the "provenance" or history and source of their plants. 'Joasine Hanet' is listed in the garden at Sangerhausen, probably the preeminent botanical collection of roses. You can see a picture of this rose on HMF. If the provenance of that plant is independent of the "found roses" and if the plant is identical in all important respects, the attribution will be confirmed.