I've argued about this before, in favour of the broad reading. The best argument is the absence of the "Pick any class..." instruction. But, as I have come to see, the grammar is not clear and cannot be parsed with certainty, because we do not know whether "any" modifies "class" or "list".
Is "any class's list" mean "the list of any class" or "any list of a class"? The former (narrow) possibility is more idiomatic.
Now, if it said "any class list" that would, unambiguously, indicate the broad option.
If it told you to choose a class and pick any spells from that list, that would, unambiguously, indicate the narrow option.
I (now) think it's easier to see the wording "any class's list" as favouring the narrow option, but it will always be possible to argue for the broad reading.
Is "any class's list" mean "the list of any class" or "any list of a class"? The former (narrow) possibility is more idiomatic.
Now, if it said "any class list" that would, unambiguously, indicate the broad option.
If it told you to choose a class and pick any spells from that list, that would, unambiguously, indicate the narrow option.
I (now) think it's easier to see the wording "any class's list" as favouring the narrow option, but it will always be possible to argue for the broad reading.