I am running AdSense on one site that does not have meta tags yet, and AdSense is showing targeted ads. That said, I agree you should have them whether AdSense is reading them or not (I just hadn't had the time to do them for that site yet).
The ads can also get thrown off-target by the text immediately above the adsense code.
Standard 3 column vanilla pages, table layout. Center is the content. Right column is AdSense. At the bottom of the content, there's a line of text that contains a keyword that's off-topic. In source html, this is 4 lines above AdSense. The AdSense tended to target that keyword.
AdSense knows the general theme of this site (judging by the ads shown two weeks ago) but is now confused about the page. Deleting the keyword has given some of those section's pages much better targetted ads.