I think any "confusion" is *probably* stemming from the fact that Stewart had made a ( well known as everyone knew ) P&D deal with Atlantic. Which if S&D were actually signed to Wexler/Atlantic it seems odd they would not have Atlantic imprints on their records. It's very convoluted? if there was a "loan" for artists services but the label being loaned the acts has a P&D with the label loaning them. I sure thought they were a Stax duo. The only way the foregoing makes *any* sense? would be if S&D were licensed "pre" P&D deal with Atlantic. I don't know the timeline? but perhaps their out of the box success of their first couple singles triggered the "later" P&D deal. curious.
Allow me to add for the benefit of others (you know this). This was the band who backed up Otis Redding!