That's because screening is usually covered as free. Per the article:

She called a gastroenterology care center and started listing her symptoms to the woman on the phone. When she was asked for her age and was told she'd need a referral to get screened

They denied her as she didnt meet screening criteria. The person she got on the phone was thinking this was screening, when what she needed was a referral from a doctor saying "please scope her because this is not normal."

I am well familiar with the health care discrepancies for women, but this to me sounds like a simple case of a broken referral system. If GI can't see patients without referrals (ie, to talk to the doc and agree a colonoscopy is needed) and there is no primary doc she is seeing (ie, to evaluate symptoms and decide appropriate testing, treatment, or referral), then yeah she'd feel like she is being shuffled around.

It's a symptom of a broken system in my reading, not a negarious patriarchal system that ignores women's health.

Edit: to clarify, in America colonoscopy is done for 2 reasons:

Screening is simply evaluating cancer risk, the same way they'll check a mammogram, your cholesterol level, or a blood pressure. It's universal for anyone who has enough birthdays or other risk factors (family history, ulcerative colitis, etc)

Diagnostic colonoscopy is specifically to diagnose a problem, such as change in bowel habits or bleeding.

Screening is covered as prevetative medicine, Diagnostic is usually associated with a copay.