It is typically better to use project-specific diversion data when you can get it, and this data should typically be accepted in a LEED review. However, there are other options.
There are LEED Interpretations such as LEED Interpretation #10060 made on 5/9/2011 that allow use of a facility-wide recycling rate, if approved by local regulators. On similar lines, a 5/9/2011 addendum added this note to the LEED Reference Guide: “For commingled recycling the average annual recycling rate for a sorting facility is acceptable for recording diversion rates only when the facility's method of recording and calculating the recycling rate is regulated by a local or state government authority.”