Well, I most certainly potty trained my child, even though they were in part-time child care! Quite easy really. Particularly on the weekends of course.
When you choose a nanny or a childcare, you are parenting. When you are up at night with them as they are sick, or have a nightmare, you are parenting. When you drop them off, lovingly, having picked someone they are comfy with, you are parenting. When you pick them up, or come home, and they run to you because they're so happy to see Mummy or Daddy, you are parenting. When you bathe them, feed them, clothe them, help them learn, and relax, you are parenting. When you shop for the foods that will help them grow strong and smart, you are parenting. When you cook those foods, you are parenting. When you help them eat those foods, talking over the day (or reading poetry like some weirdos to cover the food noises) you are parenting. When you pay for everything to make their life comfortable and enriched, you are parenting.
SAHP's do not have a monopoly on parenting, let alone good parenting.
My DH is sure as hell no less of a parent than I am. And no, he does not outsource the parenting to me.