You can do 10-15k steps on a long walk, which any active person does if not daily at least a few times a week.
Considering Carrie has been getting more and more unfit as the years went by, she's probably a couch potato so yeah those steps seem like a huge amount to someone as lazy as her.
About Alessia not posting about Ollie, I find that perfectly normal and healthy and nothing to do with Carrie. I live with my bf and have been with him for years, but he's not on my social media and I'm not on his. All the people in our lives that matter (family, friends, colleagues etc) know about our relationship, the world doesn't need to since my social media page is mine alone and so is his.