JollyK, Google's instructions once you have been approved for one site, seems to suggest you can also put the same code on any other sites owned by you.
I have to admit i find this a bit curious, and makes me think that approval at present is based on something other than the very basics of type of site, such as spiderablity, confirmed ownership, maybe time on line and a "clean" google record.
However at the moment Google is saying on one hand go ahead and put on all your sites, but on the other hand is listing those sorts of pages that you should not out it on - pages with other "text" ads, "personal" pages, SERPS, etc. most of which are quite "subjective" in terms of definitions.
If it was me i would appeal as you have, but not put in on the "personal" site until you hear back as they have beforehand explicity stated that the site does not "qualify".
As far as "blogs" are concerned generically, i dont think there is any problem as i think adwords appear on many blogger.com sites which google now owns. To me "blogs" and "personal sites" are two independent things, though some like to stereotype that all blogs are useless personal diary things. Some are, but the great majority are not.
I think the concern with "personal" sites is related to the potential for abuse (say in the case of sites which families and friends use to share news and photo's etc.. obviously they dont have the targeted demograhics that Adsense needs, and mum, dad, big brother and the dog clicking on the adsense links does nobody any good!)