Multiple sources agree that Conoclinium dissectum and Conoclinium greggii are synonymous: Flora of North America, The Plant List, USDA PLANTS Database, Flora Neomexicana III, ITIS, etc. I don't know of anyone who considers these separate species.
Where there is disagreement is on which name to use. I am not sure of the source of this disagreement, but it's really not a matter of which flora we want to follow, it's a matter of following ICNafp. Conoclinium dissectum was published in 1852:
Assuming we consider the two to be synonyms, which all sources do, the correct name is the one published earlier:
"11.4. For any taxon below the rank of genus, the correct name is the combination of the final epithet1 of the earliest legitimate name of the taxon in the same rank, with the correct name of the genus or species to which it is assigned, except (a) in cases of limitation of priority under Art. 14, 15, 56, or 57, or (b) if the resulting combination could not be validly published under Art. 32.1(c) or would be illegitimate under Art. 53, or (c) if Art. 11.7, 22.1 or 26.1 rules that a different combination be used."
Los desacuerdos no intencionados ocurren cuando un grupo padre (B) se reduce al cambiar un grupo hijo (E) a otra parte del árbol taxonómico, provocando que las Identificaciones existentes del grupo padre sean interpretados como desacuerdos con las Identificaciones existentes del grupo hijo cambiado.
Identification
La ID 2 del taxón E será un desacuerdo no intencionado con la ID 1 del taxón B después del intercambio de ancestros
Si el adelgazamiento del grupo padre provoca más de 10 desacuerdos no intencionados, deberías dividir el grupo padre después de intercambiar el grupo hijo para substituir las identificaciones existentes del grupo padre (B) con identificaciones con las que no esté en desacuerdo.
OK, folks, I'm gonna commit it...