This is not true, many specialists will not book you for an appointment without a referral, no matter what your insurance is. Call one up and try, some will book you but many will not. My friend was told to see a rheumatologist by an emergency room physician. The first 10 or so she called said she couldn't book an appointment without a referral from her PCP. She finally got one to see her with an ER referral rather than a PCP referral. A self-referral would have had no chance.

If you saw a concierge specialist that is cash pay only they'd probably see you no matter what though.