Access to Veterans Benefits Improvement Act - Directs the Secretary of Veterans Affairs (VA) to provide veterans' case-tracking information access to employees of a Member of Congress or of a state or local governmental agency assisting veterans with benefit claims. Directs the Secretary to ensure that such access does not: (1) allow the employee to modify the data in the case-tracking system, and (2) include access to medical records. Requires such employees to complete a certification course on privacy issues before receiving such access.