The 'Oeillet' fact came from a confusion written in the Manual of Roses by William Prince in 1846, a second hand specialist (and also plagiarist of Thomas Rivers) because all he did was to gather the notes left in 1842 by his father who knew the topic.
in this reference firstly you can read:

‘Asepala, Sans petales, or Rosa muscosa asepala; a new variety, something like the Provence Dianthæflora, curious, sometimes very pretty.’ (PRINCE 1846 : 19).

Then further pages later :
‘Sans Sepales is a distinct variety, with incarnate flowers of medium size, tinged with pale rose on the edges.’ (Op. Cit.: 26).

Because the flower is small and also in reminiscence of this mention, Adolph Otto wrote in his 1858 monograph, page 148 :
« Asepala (Œillet oder die nelkenmoosrose), Blumen weiss fleischfarben schattirt und zuweilen rosenfarben eingefasst; die ränder der Blumenblätter gekräufelt, klein und voll, ohne belchblätter; form kompakt, habitus ausrecht, wuchs mässig. »
Adolph Otto, 1858 – Der Rosenzüchter, Erlangen: Berlag von Ferdinand Enke
This is the most likely explanation for an imprecise or clumsy analogy with the carnation flower, not because of a direct parentage/lineage with the centifolia 'Oeillet' bred by Louis Poilpré.

PS/ I'm historian from the city of Le Mans, and i'm working on first hand local data and archives, that's why when i talk about some varieties bred from my area, it is in full knowledge.