I've written about rate of fire tests previously, in an article on the KV-9 and an article on the KV-100. Both reveal a critical component of Soviet testing. The KV-9 can fire as fast as every 12 seconds, but the rate of fire recorded in the test was only 2 RPM! The KV-100 test, which is invalidated due to all shells being loaded from the turret bustle, hints at the reason for this. The rate of fire recorded by the Soviet standard is using all ammunition racks, even the most inconvenient ones. This is illustrated well in Yuri Pasholok's book SU-152 and other SPGs on the KV tank chassis. Google around for the rate of fire of a SU-152, and you might find numbers ranging from 1.5 to 2 RPM. However, during trials, loading a shell from the most convenient rack took as little as 16 seconds (p. 132) and firing off the 10 most conveniently placed shells (half of the vehicle's ammunition) could be done with rate of fire of 2.8 RPM (p. 133). The rest of the rounds would take longer to load, but there were few instances where it would be necessary to empty the entire ammunition rack in one go. The loader would refill the ready racks when the fighting died down a little, and would be able to fire quickly once more in a few minutes.
Hopefully, that explained the "how can an IS-2 fire so fast" question. Now, for the next question. Why couldn't the IS-3 match the rate of fire of its predecessor? The short answer is "sure it could". The Domestic Armoured Vehicles series of articles from the Tekhnika i Vooruzheniye issue #11 for 2012 describes the rate of fire testing on an IS-3.
"...from June 20th to July 12th, 1951, trials were held, the results of which showed that the average aimed rate of fire with a trained loader could reach 3.6 RPM (the technical requirement was 2-3 RPM). The average cycle lasted 16.5 seconds and consisted of removing a shell from the brass catcher (2.9 seconds), loading a round (9.5 seconds), correcting the aim and firing (3.1 seconds) and the recoil brake returning the gun to the firing position (1 second).
The trials evaluated the possible approaches to ammunition racks of the gun and tested methods for loading it. The most accessible were the 17-shell rack around the turret ring, positioned towards the loader next to the fan, and the five-round rack located on a frame attached to the central contact device, as they allowed for the gun to be loaded in any position."
1. An HE shell is taken from the 17-round turret rack.
2. Another HE shell is taken from the 17-shell turret rack.
3. Propellant is taken from the 5-round rack.
4. The sixth HE shell is taken from the 17-shell rack.
5. Propellant is retrieved from an ammunition rack next to the engine compartment bulkhead.
The test and photos reveal a lot about the details of the test. For instance, we can see that loading the gun takes only 9.5 seconds, the rest, aside from the gun's return to its initial position, can be skipped if you're testing maximum rate of fire, instead of maximum aimed rate of fire. Just dumping shells downrange and worrying about the brass later can already obtain a rate of fire of 6 RPM. However, the 9.5 second figure is the average figure, for all racks. As you can see in the photo, bending down to get a 122 mm shell from the bottom of the fighting compartment can be really inconvenient. Meanwhile, the loader doesn't have far to reach in order to get to his closest ammunition. The book doesn't say how much faster loading from the turret as opposed to the hull is, but with ammunition this heavy, it has to be noticeable. It should be pretty clear that even with aiming, the IS-3 can fire much more quickly than the rate it was required to achieve according to its technical project.
Edit: Here's a little tidbit that I found, Mikhail Svirin himself writes: "The practical rate of fire [of the IS-2] in place was up to 5 RPM, on average 2.5 RPM, 1.5 RPM in motion."