I can't prove it, and perhaps I should have worded that post as more "opinion" and less "fact" but I can offer evidence:
We can assume that the existance of something implies a purpose. Either a current purpose, or one that is either forward looking or that was applicable in the past.
Of course what the purpose may be can be debated - somethings exist only because it pleased the author that it be created.
Lets assume (and it IS an assumption) that Google is interested in providing accurate and fresh results.
This would have 2 effects on its code - one, due to the vagaries of website design, there must be numerous "special case" filters and secondary processes and other code whose intent is to increase accuracy in face of a very inaccurate web filled with many who are attempting to manipulate it's code for their own benifit.
Second, in order for the results to be "fresh", code that has no use would have to be either kept to a minimum or ruthlessly eliminated, else the processing overhead would negatively affect the results for no benifit.
Also, code that had no useful component would potentially be open to unexpected exploitation.
So it is reasonable to assume that if Google is processing some data or drawing upon a resource, then that data or resource is related to the results it wishes to present.
The very existance of the "similar pages" choice in the SERPs indicates that Google possesses this information. It further suggests that the information has been processed already at some point, since upon looking at the "similar pages" list it's clear that these are not based on template similarity, or linking schemes, but rather some form of "theme".
Further, if you look at the pages in the Google "Directory" results it's also clear that while many of the "similar pages" belong to ODP catagories and are grouped as such, many others are not.
I can't think of any reason to use the amount of processing power necessary to accomplish this goal without it being relevant to the SERPs.
Although I admit that this could just be one of the side projects Google has done, it seems like a lot of work for a whim. And if it was a whim, why would it be on the main SERPs and for every single listing and not buried into the system like the Google calculator, etc?
Basically, the existence of this implies use. Does it imply that the use is to adjust PR or relevance? Not necessarily. It could be an attempt at creating an automatically generated uberdirectory. But people don't usually use directories without a search engine to help - hence Yahoo's current route. But this could be the reason - ie the Google Directory.
So you have a system that is assigning everything in it into a theme or directory - not on request like the calculator, but for everything. There is no reason to do so unless it affects the relevance or freshness (presumably).
The most logical reason would appear to be adjust either relevance or freshness. Since it would take significant processing power, it would have a negative effect on freshness, therefore it must be related to relevance.
Is this proof? No. But it passes the "gut check" on how things in a relevance interested environment would work. It would obviously also be useful to detecting FFA's and other unwanted linking strategies (as evidenced by the removal of or denigrated listings of parties in FFA's).
Do I know how much (if at all) the link's relevance is altered? No. There may be a threshold of a specific amount of links before it kicks in (likely there would be) but the fact that sites are being processed in relation to similarity is indicative of use.
Is this proof? No. More of a working theory. I just looked and this post is getting long. I'll hit send now and be happy to debate it further later. But I withdraw any statements implying "fact" and ask that they be read in terms of "opinion" or "theory". But I still believe it