I've read this thread and I disagree with your point of view. What you're basically saying is that any low-level exception that can't be dealt with correctly by the layer above it, should be thrown all the way to the top layer.
Then consider a typical J2EE application that has a simple web layer, a business layer and a database layer. If some SQL query in the database layer goes completely wrong I will get an SQLException of some sort. In your point of view the web application (being the topmost layer) will catch this exception in the end.
This defeats the entire purpose of having a multitier (3+) architecture. I'm now dependent on the database layer in the web layer, because all exceptions are thrown all the way upwards.
The point of the PersistenceException is that it keeps the tiers independent from each other, except for the tier beneath it. The web layer doesn't care if it's an SQLException. It only needs to know something went wrong with the business logic, and more specifically with the persistence of business data objects.
In any case, the 'business code' knows more of what to do than the layers above it. If it can't do anything meaningful with it, you can either log it or perform some other action. The question is: what would a layer above it (eg. the web layer) know more of what to do than the business layer?