That's what Thorek is claiming, yes. When the time of Woes made the hold unsustainable, the poorer clans were sent to beg charity and refuge from the Karaz Ankor, whilst the wealthier clans used their money and influence to obtain comfortable lifestyles within the Empire.
Now the thread can argue back and forth how accurate that claim is all day, but the fact is that the hold split into two groups; one group stayed within the borders of the Empire and became wealthy, and one group migrated across the continent and became destitute. Dwarf culture demands that the wealthier clans use their wealth to support the poorer clans (we learned that with the "potluck alloy" from the festival we attended with Johann), and the clans that stayed appear to have been failing in this duty, which is grudge worthy by itself.
Now, we should line up what else we're told in various sources, which may or may not be accurate.
The neighbouring polities of Laurelorn and Karaz Ghumzul declare independence from their respective imperial metropoles during the war between them. Note how it's Karaz not Karak Ghumzul. They're claiming to be a peer of the Karaz Ankor by this I assume.
An army from Karaz Ankor goes to attack Laurelorn anyway, Karaz Ghumzul refuses to help, and said army vanishes without a trace in the forests. Elven magic is blamed/credited.
This is around -1,500 IC. At the same time the Belthani are recorded crossing into the northern Old World for the first time by the dwarves according to the Tome of Salvation.
Some five hundred years later, around -1,000 IC, the proto-Imperial tribes are recorded to have crossed the Black Mountains for the first time by the dwaves garrisoning Black Fire pass, entering the Reikland basin.
According to Tome of Salvation, at some time later the Teutognens discovered the mountain that would have Mitgard and then later Middenheim built on it. The temple was completed there in 63IC.
Now, we have other sources. According to Ashes of Middenheim, Tome of Salvation's sources are wrong. The settlement that would become Middenheim was founded in -50 IC, after a neighbouring dwarf clan helped the Teutognens tunnel up through the rock to reach the summit, and the temple started construction in 63IC and was finished in 113IC. The book later goes on to say that's just what the human inhabitants claim, and they're wrong. The dwarves know and they have evidence that the rock was a dwarven gold mine/settlement called Grungni's Tower that they'd occupied for centuries before the humans arrived, during which time they'd warred with the skaven in the depths. I would trust dwarven records and physical evidence of presence more than human religious and ethnogenic myth building from before they were literate.
Thorek, by contrast, says that the dwarves of Middenheim are refugees from Karaz Ghumzul who paid the humans to take them in.
This leaves a long gap. Even according to human records, humans only occupied the rock of Middenheim from about fifteen hundred years after the Time of Woe, when Artur of Teutognens founded his settlement / it was explicitly unoccupied by humans before then. Now this was just as the dwaves we're entering their silver age thanks to human allies - it's worth noting that there are other references to the proto-imperial tribes serving as auxiliaries to the dwarves, so this may have been in progress before Sigmar.
If the dwarven records mentioned in Ashes or Middenheim are accurate here, this suggests there's a lot more to the story than Thorek suggests. Was Grungni's Tower originally in the territory of a Belthani group? It seems unlikely that the dwarves would have bothered to get the permission of some shoddy Stone Age nomads to excavate under a mountain, but it's possible. If so, the dwarves must have survived at least five hundred years of the Time of Woe for there to be any humans around for them to deal with.
To add an extra mystery, Belthania is an elven given name in Warhammer.
We also know that the location of Grungni's Tower would have been pretty close to Laurelorn's then borders. So, what I'm wondering is if there may have been continued contact/friendship between the rebel dwarves and rebel elves after they declared independence, possibly with the involvement of some human clients, which may be connected to the continuing human worship or what looks like an elven god in the region. We've had references to some longbeards seeing history as a stone to be worked, which suggests that while they wouldn't make things up, selective forgetting may well be on the cards, and an alliance with the elves of Laurelorn is the kind of thing that might go down the memory hole.
All speculation of course, but if Karaz Ghumzul did fall during the period of known human occupation of Middenheim it does mean that the dwarves of Middenheim may actually not know how to get back into their old parent hold. They may just be claiming to be the de jure successors, but their ancestors may have been their centuries before their capital fell. Depending on the sequence of events and the disposition of forces at the time, it might partially explain why the refugees of the capital fled to the Karaz Ankor while some clans survived under Middenheim. By this point the broader Karaz Ghumzul may itself have fragmented, or there may have been enemy forces in the way of them reaching the established settlement of Grungni's Tower. It may even have been under siege itself.
We may also be poking a hornets' nest politically, if the dwarves of Grungni's Tower consider themselves to be the legitimate successors to the independent nation of Karaz Ghumzul, and not bound by the submission/defection of the refugees back to Karaz Ankor. For example, if the dwarves were there first, do they consider themselves Imperial subjects, or as gracious hosts and allies who have generously allowed men to live on top of their home. Unlike Imperial dwarves elsewhere in the Empire who may have sought refugee with humanity, from the Middenheim dwarves' perspective it may be the opposite.
All speculation of course. I would generally be hesitant to just take Thorek's view on the matter without considering the potential other viewpoints though. We may well find the perspective of the descendants of Karaz Ghumzul just as sympathetic as those of Laurelorn if we knew their story. One man's traitor is another's patriot after all. If the Middenheim dwaves turn around and grudge the fall of their state on the Karaz Ankor treating them as a rebellious province in need of reconquest rather than as an independent peer for fifteen hundred years, I'm not sure we can really blame them given what we know. Thorek has just got through telling us how through a job that dwarves can do of blackening each other's names for political reasons.
Given their proximity, and how valuable a surviving even if unfriendly Karaz Ghumzul would be to Laurelorn, our current hosts may have a well informed perspective.