Just for example, you could download data, compute the hash, then delete the data. You could pretend to have stored lots of data this way. If someone asks for the hash to prove that you have the data, just give them the hashes you computed earlier. That's what the first paper prevents.

Another one is to pretend that you have lots of chunks, and when someone challenges you to produce one, you quickly download it from another source and present it as if you had it all along. That's what the second paper prevents.