Imagine if the "trusted domain" used for the whitelabel site on a subdomain was google.com. Constantly referring to "Google's algorithm" misses the real issue. Google can do whatever it wants. Google can "trust" anyone or no one but itself. Google has all the traffic, not the coupon websites. Do we need laws that govern such middlemen?
"Google can do whatever it wants" - wouldn't this be anti-competitive behaviour if they stated favouring certain sites in their algorithm? I seem to remember reading somewhere that they get audited to make sure they don't do this, although can't find the link.
What I would expect to be illegal would be overly favoring their own sites/services over those of competitors, since they are so big and that would be abusing their search marketshare to spread into other markets.