Kevin
You're correct the overridding metod in the subclass can not throw any exceptions higher i the hierarchy then the method it is over riding. In this example aMethod() in SomeClass has placed the code in a try/catch block so it doesn not have to put the throws clause in its definition. Calling it from AnotherClass is also ok because the exception is fully handled in the base class. If it weren't and the base class method could throw the exception back up the call stack then it would also have to declare that it throws the exception and then it would be ok for the sub class to do the same.
The code as they have described it doesn't compile. So that answer can't be correct.
What version of the book do you have? I have the same book and don't remember anything in that chapter as odd, of course you could be more observant than I am.

Now I'll have to go home at lunch and check my book out too.
Dave