Disagree, strongly. 'Sandbox' is about trust via links. It applies on a page by page basis. Seen and studied it across 70+ new sites over the past 2 years.
What people call the sandbox effect is just an extension of how Google normally puts pages into its primary and secondary indexes.
If you need links to get into the SERPS for a term (primary index), you won't get in that index until Google sees enough decent trusted links. An interesting factor that also comes into play here is the way that Google returns pages for three or four word terms if one of those words is highly competitive. If there are enough sites in the primary index (which relies heavily on links) then you won't feature in those results even if your title tag and on page SEO is 100% on that specific phrase. Drill down the SERPS to the point where you start seeing irrelevant sites and you won't see your page. It just doesn't meet the criteria to get in. Not enough trusted links.
Best example :
I launched a site for a client in the debt industry about a year ago. He has pages about different problems and the various solutions. One page was about bailiffs. After I had optimised the site that page ranked top three for 2 or 3 terms within weeks. He got so many calls about bailiffs he told me to back it off - people being pursued by bailiffs weren't his target market (no money!) and he didn't want that sort of business. That's why it was easy to rank - no-one else wanted those terms so it was secondary index and on page SEO was enough.
All his other pages feature(d) the word 'debt' somewhere in the title tag or in the page. Even if I searched for very long tail terms I never saw them - because all of those results were pulled from the primary index.
If you can get links from truly trusted authority sites then you can shorten or skip this 'probationary period'. I have an idea that the length of time 'probation' applies is related to the competition for those terms.