You can look at a blog post about why there was confusion about Phebe Coulton's parents here http://myfamilyresearchadventures.blogspot.com/2008/09/phebe-coulton.html
The record I found about her parentage is:
This record can be found on Ancestry.com in their Quaker collection. It is a digitalized copy of a Darby Monthly Meeting. Source Citation: Swarthmore
College; Swarthmore, Pennsylvania; Quaker Meeting Records; Call
Number: MR-PH-141.
The third paragraph down reads:
Whereas Phebe Robison Daughter of William -
Coulton and Phebe his Wife was Educated in the profession
of Faith as held by us. But giving way to a Libertine spirit
hath been so far Led into Error as to suffer herself to be Joined
in Marriage by a Priest to a person not of our Society to the
Reproach of our Christian Profession, and Contrary to the
good and regular Order Established among us, Notwith-
standing she had been advised and Precautioned to the Con-
trary.
