Google is a search engine - it does not own any of the content it indexes (other than content it owns). I'm not sure why people cannot make sense of this.
As a user you put a query into the search box and Google has the task of filtering through trillions of webpages to find the "best" results. There are countless webpages that Google does not filter through (because the creators deny Google access or because Google can't discover them). That is the extent of what Google's search engine does. Once you find a satisfactory result, you click on the link and Google is thrown out of the picture all together when your computer makes a request to the server Google found for you.
At no point does Google prevent your computer from requesting information from any server - it can't in the same way a phone book cannot prevent you from calling any number you want. If access was blocked it would most likely be from your ISP, a computer virus, or an attack on the server itself (usually by the government).
It's just ridiculous to say Google shouldn't be able to censor its search results, the entire idea of search indexing is based on valuing certain content more than others. A "Blacklisted" website is not censored information, it's a denial of access to the results page, which every website is technically subject to for the majority of result pages.
Soon they'll be accusing Google of censoring the ads it places on websites...
Some are upset at Google for what they believe is censorship of certain content. Google, however, as a company has the right to regulate content that may be detrimental to its business. Google must keep shareholders, customers and users all happy in order to remain a profitable business. Therefore, it does have a reason to ensure that content accessed through the search engine does not upset its business interests.
A private company has the right to regulate its content if it serves the best interest of the public. For the sake of national security, Google has the right to censor sites that promote extremism, or shutdown thise that promote child prostitution. All these serves the best interest of the public.
Despite the fact that Google is a privately held company, it has a responsibility to the people who use its service. Individuals use Google to provide them with information. They depend on the search engine to connect them with what they're looking for. When Google censors content, it prevents its customers from having a full experience with their service.
Google, as one of the major Internet companies, should be pressured to fight for the free flow of information. If Google is allowed to censor its content it could spell disaster for the Internet as we know it today. Just ask yourself, if they are allowed to censor now, will there be a possibility of drawing the line with their self-will in the future?