The text you've quoted is specific to codeshares and not applicable to your situation. What it says under SQM is "SQM are Status Qualifying Miles. You earn them by taking flights with AC or Star Alliance airline partners." SQS/SQD say the same thing.

AC offers many flights by non-*A airlines on its website. As big as *A is, it doesn't fly everywhere, so sometimes the only option is a carrier outside the alliance. It's also not a single integrated airline, with each airline cooperating to a certain extent, but also looking out for its own bottom line.

This occasionally leads airlines to form partnerships outside the alliance. For example, AC and AI are both in *A, but for various reasons, AC has chosen to partner with EK and funnel a lot of traffic to/from India via DXB. Or in the old days, AC often had better pricing to South Africa connecting via LHR on BA than it did with SA.