Yes, Zinnia hybrida is a synonym for Z. peruviana.
http://www.catalogueoflife.org...
It's not a matter of taxonomic authorities not accepting the work of academic authorities, and that's not what I said. I'm saying that academic authorities may accept a species name when taxonomic authorities do not accept it. Most of the taxonomic databases list only the hybrid taxa that occur in the wild and do not list the names of "man-made" hybrid taxa.