Greenie - first off I dont think that the 403 on the index would cause a removal - only if the 403 occured on the free site itself - I really dont care what they have on the root index unless its something objectional/against the rules - and Im pretty sure the bot you use doesnt check the index page on the root - just the sites listed - but that may just be something youre doing on the side that I didnt know
As far as the SE stuff - first - the keyword here is knowingly - and Id say that in pretty much every case Ive looked at where someone has posted that a domain is banned in Google - it was not - someone had looked at Google using thier little script tool or some other sites tools and decided that it was banned - which in Google is highly unlikely and very few and far between. Unfortunately a lot of "SEOs" have decided that Google bans sites/domains for all types of reasons - and this just isnt so - they may hand remove a domain/site based on some spam reports from the index - or go so far as to supplemental out some pages based on dupes - but banning at Google really is saved for extreme cases. Now if they are "not listed" that is a different scenario and can be caused by reasons ranging from not being crawled properly, not enough time since first crawled to be included, not linked to properly etc etc - hundreds of reasons - but none that would stop me as a linklist owner from listing the site.
I have looked at the tools that some of the "knowledgeable SEOs" are using to determine if a site is "banned" by Google, and all it checks is backlinks (which Google has already stated is fake), PR (which again Google has already stated is faked in the toolbar) and occasionally they mine into some areas of Google that they "interpret" to their liking for indicators of "bannedness"
So as I said - the keyword here is knowingly - and quite honestly there is no way to "know" because Google aint gonna tell ya