A "shielded loop antenna" is a very misleading name. It isn't an antenna, with a shield. It's an antenna made from a shield, with a feedline inside it.
It's commonly stated that the shield blocks electric fields and not magnetic fields. But that's false: it's physically impossible. That's not to say that a shielded loop antenna has no merit beyond an unshielded loop antenna, though. The "shield" makes an excellent, broad-band, low-loss, easily fabricated balun.
There's an analogous problem with dipoles also. If we want to feed a dipole with coax, we need a balun to prevent common-mode currents on the feedline, because if there are common-mode currents on the feedline, the feedline is part of the antenna.
We could build a magnetic loop antenna like this:
simulate this circuit – Schematic created using CircuitLab
The feedline is balanced, and the antenna is symmetrical. Like a dipole with a balanced feeder, there are no common-mode currents and the feedline will not radiate, provided the surroundings are also reasonably symmetrical.
But we want a coax feedline.
There is only one place to connect the coax that won't result in common-mode currents: immediately opposite the feedpoint. If we do this, then any common-mode currents will cancel at the feedpoint. With any other arrangement, common-mode currents can couple into the feedpoint, so the feedline will be part of the antenna.
But then how do we get the end of the coax to the feedpoint? The solution: make the antenna from tubing, and run the feedline inside the antenna. Because RF currents travel on the surface of the antenna, what happens inside the antenna is irrelevant to the operation of the antenna. Electrically, it looks like an ordinary loop antenna made from fat wire.
Modern Antenna Design by Thomas A. Milligan describes this as a natural balun (though, I've never seen that terminology used elsewhere):
A natural balun feeds the coax through a loop antenna to the feed point where the outer shield is split and the center conductor jumps the gap to connect to the outer shield of the coax. At this point the currents flow on to the outer shield and radiate. By moving an equal distance along the coax until the two halves meet, we can connect the feed coax and not have current flow down the outside. The currents flow in opposite directions along the loop and cancel at the connection. From a circuit point of view, the connection point is a virtual short circuit to the balanced mode similar to a folded balun at its connection point. In a similar manner, on a folded dipole we can connect the feed coax to the middle of the shorted dipole and form a natural balun.
If we simplify the construction a bit and double the coax shield as the tubing, this type 2(d) from the question.
As it is, this design has a coax feed and no problems with common-mode currents. However, if one wants to add a capacitor to resonate the antenna at the operating frequency, or a matching network, one must be careful to preserve the current balance of the antenna. The ARRL design is notably horrible at this. However, we are getting away from the topic of the question, so I will suggest reading W8JI on small magnetic loops for a more detailed discussion.