This is directly in line with what happened to me when my first Wii was stolen. I had a huge library of Virtual Console/WiiWare titles purchased on my console and was hopeful to getting them restored once I purchased a replacement Wii. I contacted Nintendo support, provided my previous system's serial number and other information, verifying that it was my console. Then they asked me to fax them a copy of the police report--a police report that was never filed, would cost money to obtain a copy of, is just a hassle in general. I have hundreds of dollars in software I purchased, and Nintendo won't side with me until they see a report with that Wii's serial number on it.
I really should just go ahead a file a police report years after the fact. It'd be nice to be able to get to access all those games again. I was really hoping the Wii System Transfer Utility would have been able to access your Club Nintendo account and pull your digital purchases from there, but it's all dealt locally. If I want to get my Wii Virtual Console and WiiWare games on my Wii U I have to file a police report, purchase a copy of it, fax it to Nintendo, give them my new Wii's serial number, redownload everything, then use the System Transfer Utility. What?