How do I indicate that I am insured under my parents' health insurance?

You don't have to enter anything in the federal return.  If you are in the MA return:

1. On the screen, When did you have minimum creditable coverage (MCC)?  mark the radio button, My health insurance met MCC all year.
2. Answer the rest of the questions about your parents' coverage, since you are covered under their policy.

What do you mean "MA" return?

If you mean my state return, if I recall correctly, my interface did not have a separate section for federal and state. That question was never an option for me to answer. Now when I am amending it simply has a "revisit" button option beside each option of "Personal Information," "Health Insurance," and "W-2 Income," in that order. I click "revisit" on Health Insurance but the website takes me to the Personal Information section instead. Then I click "Continue" and it skips over the Health Insurance section and goes straight to W-2 Income. 

I am puzzled. Why are your saying that "Now TurboTax thinks I am uninsured,"?

Is this on the federal return or the state return? Is there an error message?