How much influence does Goodman Brown’s companion claim to have?

As Goodman Brown and his fellow-traveller traverse the
path to the forest primeval, the older man who carries a staff bears an uncanny
resemblance to Goodman himself yet he has the air of "one who knew the world," and would
be comfortable in the company of the governor or in King William's court.  As Goodman
talks with the stranger, the elder tells Goodman that he has been well acquainted with
the Brown family as well as many of the Puritans:

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I helped your grandfather, the constable, when
he lashed the Quaker woman so smartly through the streets of Salem; and it was I that
brought your father a pitch-pine knot, kindled at my own hearth, to set fire to an
Indian village....They were my good friends,
both....

In addition to
these, the traveller says that he has known many a deacon  who has "drunk communion wine
with me," implying that they have in attendance at the black mass with him. Ironically,
when Goodman Brown runs off lest Goody Cloyse see him with the elder man and ask who he
is, it is Goody who recognizes the traveller and greets him, "The
devil!"

Of course, it is the traveller/devil who is at the
black mass where Deacon Gookin, Goody Cloyse and the others attend. So, in effect, the
traveller with the staff (the devil) has great influence upon
many.