Apparently you need an adwords account 'in good standing', I'm not sure what they mean by that because we do have an adwords account, and as far as I know and can see it is in 'good standing', only we're not advertising any more using google because we found that it isn't making enough money in return.
See:
http://news.ycombinator.com/item?id=1593898
I'd pay for analytics, it's a very useful service and I can't see the adwords angle, after all with something as vague as 'good standing' as the deciding factor how about simply charging for analytics?
I always figured that analytics was free because it provides google with useful data as well.
Maybe it's time to get my old stats suite dusted off and re-installed, I don't like operating against the TOS even if it is apparently something they'll let you get away with.