Google does not search all publicly available information - it only searches information from publicly accessible websites. If information is only available for a fee or with a password, then it is generally not going to be searchable by Google. While BeenVerified does not have access to all public information either, it does have access to these for-pay and password protected records that regular search engines don't have access to.
BeenVerified has access to databases that would otherwise require many expensive payments. For the price of a single BeenVerified search, you get access to information that might otherwise cost multiple fees and require many searches. This type of information includes civil court documents and government records. It also includes criminal records that do not generally appear on a generic Google search.
Google returns searches by relevance, but does not exclude irrelevant information. When you run a Google search for someone using their identifying information, it may return searches for people who share the same name, people who share the same birthday, or other identifying factors. The results may not be for the person that you’re actually trying to find.