Scenario - you have a site that has been a steady performer in Google for years and you begin work on a second COMPLETELY unrelated site that WILL NOT LINK OR MENTION the first site in any way. Suddenly site #1 traffic takes a tumble just as you are rolling out site #2. Though the two should be independent of each other you know they are linked in places like adsense and analytics as well as hosted with the same host, on the same server and both made by you.
Not being linked together on-site in any way should be enough to avoid any rankings relationship but when you pull ads off site #2 you notice that traffic trends upwards again on site #1 over the span of a few days. Two weeks later you put the ads back on site #2 and there goes site #1, again.