I think in the context of this thread it is the Aikikai terminology that is being referred to. There is no real connection to the Daito-Ryu groupings.
You are right.
When I get bogged down in doing a technique, I find it freeing to remember Aikikai is a very new organization. We're referring to a name that is maybe only from the 1940s, maybe even later. My own teacher did show very ikkyo derived stuff that were called kokyunage or koshinage. There are many variations on a theme that Aikikai calls the same name and they all claim similar lineage and history.
When I read a dokka accredited to O Sensei that reads Ikkyo can take your whole life to perfect, I give myself a little license. I feel I get trapped when I try to strictly define a movement as one singular variation and thing. I like ikkyo as I learned it; I learned something different than I was taught for oshitaoshi last weekend when I took a seminar from another organization.