I was surprised by the claim, so I looked into the linked source: "You would be exposed to about 0.035 mSv (3.5 mrem) of cosmic radiation if you were to fly within the United States from the east coast to the west coast. This amount of radiation is less than the amount of radiation we receive from one chest x-ray."
I note that it says _less than_ in the source, so let's compare the actual numbers -- it's 0.035 mSv for the flight (from the first source) and 0.1 mSv for the chest x-ray (from https://www.cancer.org/treatment/understanding-your-diagnosi...). It does seem fair to say they are similar. The cancer.org source also notes that you'd normally be exposed to about 0.1 mSv naturally over the course of about 10 days. So we can say the flight from NYC to LA is ~4 days of natural radiation exposure.