This is the very thing that Google is saying that Bing is stealing with their clickstream data, and it's also the one that you're agreeing would occur - "that the only relevant info is coming from the toolbar" for highly unlikely queries.
So it seems to me, looking at your argument, that you actually agree with Google's point.
Google is trying to argue a huge PR point by saying, "Bing copies" with the ramification being that when you search on Bing you're really searching on Google. If Google said this, "For extremely rare searches where Bing has few, if any, good signals, clickthroughs from Google will be weighed in such a way that these results may make the first page".
I'd buy that 100%. The Bing team may even buy it. Google seems to want to start with that thesis, but then try to shove the whole camel in too.
This is pretty straightforward and I'd be surprised if Google didn't have the infrastructure in pface to do this today (like literally today).
Also do things like 'radix-2 fft', something where there is a lot of additional signals (I suspect), yet something that other toolbar members probably aren't searching for. So the toolbar data MS gets is strongly skewed to your results.
The should search for Justin Bieber and add in the Bieber search results some really horrible link.
MS should have a lot of relevant info for Justin Bieber, so the Google data should be rated lowly. If this non-sensical result makes the first page then you can begin to assume that their weighing it heavily. But when your query is "erftqnvpwedf" -- that just means that the only relevant info is coming from the toolbar. Bing would show that result even if the toolbar only accounted for 1/(2^50) of the total relevance.
I suspect Google did this test and has nothing to report.