Yes that's true .. as google is very strict about content and others ..and if your website or blog found as a policy violation then your google adsense ads serving ads disable.
I also had a similar situation. One of my domain get banned from adsense but other website are running with adsense ads.
I dont think so that it is possible. if an account is banned then it means that you have to try for a new account. I never heard partial blocking of adsense ever.