Possibly this is a (mistaken) extension of the idea that once summoned for birkath kohanim in the synagogue service, a Kohen who declines to perform the blessing is in violation of the positive commandment to bless the people:
Shulchan Aruch 128:2
Any Kohain to whom one of the inhibiting factors does not apply who does not go up to the duchan, even though he has annulled one positive commandment, it is as if he has annulled three if it was when, in the Beit Hakeneset, they called, "Kohanim," said to go up, or told them to wash their hands.
See also Biur Halacha 128:4 which is cited by Halachipedia as:
If a Cohen is in shul and isn’t called up to do the Birkat Cohanim, strictly he isn’t obligated to do Birkat Cohanim (certainly, it’s appropriate and correct to do so) however, once a Cohen is asked to do Birkat Cohanim he violates the biblical command by refusing.
(Bear in mind that, as the Shulchan Aruch lays out in the very first halacha of Siman 128, Birchat Kohanim is only ever possible in a minyan.)