One reason to justify Google's cut is that on an advertising deal where the Advertiser gets billed for each click (CPC) on his link on someone else website, having a reliable third party to count the clicks is very important.

Click fraud is what makes Tier 2 CPC networks really risky for advertisers even if CPC are much lower than Tier 1 (Adwords, Bing).

Regarding your Adsense example, was there not a mention like "Ads by Google," "Sponsored Links," or the AdChoices icon ? In that case, it makes clear that it's not a natural link.