W8JI's view, as I understand it, is that small shielded loops are no
less susceptible to local noise in virtue of their shielding, since
the shield, in his view, is part of the antenna. It's probably worth
pointing out that, even if this is true, it is still consistent with
the view that small loops pick up less noise than other types of
antennas in virtue of their directional characteristics. I guess W8JI
would then maintain that a shielded loop would be no less susceptible
to local noise than an unshielded loop, since in this case both
antennas enjoy the benefits of directionality; but he isn't commited
to denying that loops are quieter than, say whips when all things are
considered. Is this correct or am I missing something here?

Correct. Here it is from VE7SL perhaps more concisely:

Please note that a 'shielded loop' will not do anything to improve local
noise problems that any other type of loop (such as a multi-turn air core
loop) might do. Don't confuse the 'shielded' nomenclature with 'noise
shielding' as this is not the case. Like any other type of loop, it can be
used to null nearby noise sources or signals or turned to enhance desired
directions.
The shielded loop might more properly be called a 'two-turn' loop or a
'close coupled' loop as this more accurately describes it's behaviour. In
actual operation, it is the shield itself that is the active antenna
element. Signals picked up by the shield are coupled into the inner
conductor, which in turn are coupled back to the receiver via the preamp.
The loop is capable of good nulls on both groundwave and skywave signals.
The more 'balanced' the loop is (gap placed at exact center), the more
balanced the nulls will be.