This is factually inaccurate; contracts are one area of, but not the basis of, common law.
> In the eyes of civil law, the use of the site would need to take place per the laws and regulations present in civil law as opposed to whatever that the user may agree in terms.
In common law, contracts don't trump other law, and contracts or provisions thereof can be invalid for being contrary to public policy.
Of course it isn't the entire basis of the law. However it lies in the fundamental of the entire common law institution: Common law originated from the feudal relationship in between the liege lord and the vassal contracting each other based on certain criteria. Over time, this concept was meshed with medieval customs and started being applied to the society as a whole. Hence the awkward medieval-feeling nature of the common law with all those 'precedents', 'interpretations' and 'agreements'.
> In common law, contracts don't trump other law, and contracts or provisions thereof can be invalid for being contrary to public policy.
Today. And mainly because the US combines common law and civil law in a meshed system. For the UK, its mainly because common law was basically unworkable and indefensible in the modern age after civil law became de facto standard in the entire world, setting the legal discourse. Still, the contractual concepts lies in the fundamental of the law as evidenced by the 'agreement' concept that is so extensively being utilized by US corporations.
That's the Angloamerican common law's logic. In civil law, the law cannot be overridden by others 'agreeing' to override it. Its more like software engineering in that regard, instead of arbitrary interpretations.