A thousand times no. Reg E 1005.11(b) requires that the customer provide their name, account number and describe why they believe an error existed. It is the burden of the bank to obtain documentation to demonstrate that an error did not occur, not the customer's responsibility to prove that an error did occur. The bank can request, but not require supporting documentation from the customer to aid in the investigation.
The CFPB put it best in their Fall 2014 Supervisory Highlights.
"Regulation E also sets forth the timing and content requirement to assert an error, specifically, sufficient information to identify the consumer’s name and account number and why the consumer believes an error exists, including, to the extent possible, the type, date, and amount of the error. A financial institution cannot deny an error claim on the basis of a consumer failing to provide additional information, or require the consumer to contact the merchant involved first."