Why don't my tied hashes make the defined/exists distinction?

They may or they may not implement the EXISTS and DEFINED methods differently. For example, there isn't the concept of undef with hashes that are tied to DBM* files. This means the true/false tables above will give different results when used on such a hash. It also means that exists and defined do the same thing with a DBM* file, and what they end up doing is not what they do with ordinary hashes.