Indeed, that is correct.

I flew on CO equip to Paris last year, but booked on the AF code because I was connecting to BCN - CO does not code-share the connection. So despite CO equip, no status miles since it was not booked though CO. Same applies to AZ as to AF.

Note that NW and HP are different - status miles for all flights under those codes - even operated by other cos (e.g. KLM equip on a NW codeshare).