A legal problem with planting a cookie in another site's domain

[James Firth]

Either way gentlemen, my argument was for a website that wasn't providing an
information society service that had reasonable grounds to use cookies in
provision of said service.

A POW (Plain, ordinary website) with a privacy policy "we use no cookies and
store no information about visitors".  Visitor goes to website and finds
cookies under the website's domain.  Grounds for a complaint against an
apparently defective privacy policy?

James Firth