As for the article in the OP - while choosing is good, if you drop into a small hospital having made no contact ahead of time, you may be limited in who is there to treat you, and they won't know anything about your preferences either.
Actually, the article is very clear that on arriving at the hospital, the OP requested only female HCPs.
It is also very clear that any woman can refuse an examination of her cervix for any reason. Medical treatment is by consent.