Checking curtain rod stability?
If you have pulled on them and demonstrated that they are sufficiently solid, it sounds like you have a relationship issue involving physics vs. "alternative facts".  

Personally, for anchoring in wallboard, I prefer "zip-its", also known as auger anchors, tornados, and even wall-drillers, based on their part number at a certain manufacturer.  

By the way, the plastic sleeve anchors that your partner likes are, I believe, better suited for cinder-block and concrete.  In plaster-board, it's zip-its or toggle-bolts that you really want.