Isn't it a bit quick for a law suit, even by US standards?
Has Google refused to refund? It seems a plausible circumstance for an app to measure data incorrectly. Have Google refused to prove their App is considering the correct counters?
How far back in time can people check they were using the network they thought they were on? as stated in earlier comments, people can, and do, use the cellular networks over wifi without checking, particularly if your cellular data is relatively fast and reliable. Some phones I am sure will try to multiplex data from different networks... I C U Apple...
I feel certain that such a basic issue would be flagged up by more people though, there don't seem to be too many similar complaints around...
I note the complaint says he downloads 6-11Gb month on his phone - I assume he is either an avid movie watcher or using his device as a hotspot. It seems rather a lot to me!