When I go to the homepage, the site certainly wants to send me a cookie...

... which I refuse, of course, since such a cookie is of no use to me.
However, Cyveillance's Privacy Policy states the site does not use cookies,

which is obviously a lie. Or is it?
Maybe, maybe not... When you refuse a cookie on accessing the site (home page), accessing another file (such as images linked to from the same site) or accessing another page (such as the Privacy Policy page) does not result in renewed attempts to set a cookie:
But of course when a cookie is accepted, it is stored, and the browser will subsequently send it back to the site with every HTTP request:
Which means that --as long as you do initially accept a cookie-- that cookie certainly can be used by Cyveillance. But they might ignore it as well.
Yes. Of course, if they didn't try to send you a cookie in the first place, you could be sure cookies are not used, as stated in the Privacy Policy. But if a cookie is sent and accepted , it certainly can be used to track you through the site. Which means that the Privacy Policy certainly is lying when it states that cookies "cannot" be used to track a visitor's path through the site. They can be. But no one (but Cyveillance) can know whether (accepted) cookies actually are used.
I'd suggest Cyveillance stop trying to send cookies completely.