The short answer is no. Each credit bureau maintains their own seperate database of consumer credit information which they use to populate their own consumer credit report. The strength of their database directly impacts the sales of their credit reports and scoring models so it is not always in their best intersts to share the information. In fact, often times the bureaus will compare their credit report with a competitors in order to win over more business.
That said, they do work together in some aspects in order to bring more standards and accountability to their industry. One example of this cooperation is the Consumer Data Industry Association (CDIA). Representatives from all four major credit bureaus attend regular meetings of the association to help being more standards and accountability to their industry. The Metro 2 Format was a cooperative effort between all four bureaus as was the creation of the E-OSCAR system for automated corrections to consumer credit files.
While the bureaus remain competitive with eachother, they also recognize their impact on individual consumers and strive to encourage high standards for maintaining data integrity as an industry.