This patient expected a free checkup. The bill was $1,430.

Updating immunizations is also a common covered service at these appointments. The vaccine for HPV, or the human papillomavirus, provides protection against an infection that can cause several types of cancer. Federal health officials recommend being immunized for HPV at age 11 or 12, though the vaccine also can be administered later in life. A patient who needs blood tests for a specific medical concern — as Aiken did, for medication monitoring — could be required to pay part of the bill. That’s the case even if the blood test...