The DMCA basically states that its a big web out there and that content moves around. You can't be sued up front for holding content. Content is different from a copyright infringement (ie you try to pass yourself off as Ford Motors). YouTube gets hundreds of DMCA notices a month to take stuff down. Now if you ignore the notice, you can be taken to court. There is not big registery out there that lists DMCA's like a credit ranking. Your whole site will not be taken down because of a DMCA notice. It holds no legal grounds to remove a site. If you are asked to take something down, require proof, that is allowed under the DMCA. If you get sued, you can defend yourself under the DMCA. It works both ways.
I run a wallpaper site and I've received a DCMA takedown notice from Playboy. They didn't file and charges just asked for the content to be removed within 48 hours. My host (mt) called me over the phone to alert em of the DCMA Takedown and that they themselves would delete the content if I didn't get to it in 48 hours. Wasn't that big of a deal, just be careful.
There are many inconsistencies and wrong information in your post. You are thinking of trademark infringement. Copyright infringement is specifically related to content (text, images, videos etc.). If you use any of these without permission from the copyright holder that is copyright infringement. The DMCA only applies to sites that have a registered copyright agent with the US copyright office and that meet the safe harbor requirements, and contains content uploaded by users of the site. This only applies if you have a registered agent. If you don't then the copyright doesn't need to send a DMCA takedown notice and requiring a formal DMCA notice is just a waste of time for the copyright holder. Depending on the severity of copyright infringement a host can definitely take down an entire site (if for example all the content is copyrighted content used without permission).
you obviously don't know that your host could have taken down your entire site without telling you first... or maybe losing your adsense account is no big deal either, how about getting arrested for scammer links?: According to US Today, Google said in a statement: "We take copyrights very seriously. In accordance with our policy, we disable ads on websites in our content network when we are made aware that they appear next to copyrighted content. Copyright holders who find their copyrighted material appearing next to Google ads can find more information about the Digital Millennium Copyright Act (DMCA) take-down requests on our AdSense website. Hundreds of thousands of website publishers responsibly abide by our policies and we're committed to preventing those who don't from using our program." http://linksandlaw.com/news.htm "TV-Links.co.uk, a TV and movie link sharing website, was full of links to pirated TV shows on sites like YouTube, MySpace Video, DailyMotion etc. The site was recently shut down and the owner arrested in the UK. See: TVLinks Shut Down By Authorities | Owner Arrested On Copyright Violation Charges" http://linksandlaw.com/news.htm