Yes, some clays turn to mush, but that just depends on whether the clay material was fired or not and at what temperature. But this has little to do with how it grows plants. Take a look at the ceramic tile on your bathroom floor or in the planted pot out on the terrace, or even the bricks used to build your house/pond. These are all clay dug up from the ground and, in their pure state, if you leave them in water for months they turn to mush. But if you put them in an oven then this changes their structure and they become what we call ceramic, brick or pottery, impervious to being soaked.
Laterite clays are typically rich in Aluminum and Iron, which leeches from the mineral rich rock sitting above them over eons. The iron oxide is the reason that the color of the clay is red, that's just rust. 20 years ago everyone was hysterical about Laterite because of the iron it contains. Laterite was the "In" thing for planted tanks, but people didn't realize that the reason Laterite was a good substrate was because it was a clay with decent CEC, which is a property that conveys nutrients from the surrounding water to the plant roots. And that is much more important that the fact that it contains Iron.
Bauxite is a variety of Laterite, and Bauxite is mined aggressively for the aluminum it contains. In fact, that's where most of the aluminum that we use comes from.
So whether it's fired to harden it, or whether it's found mixed with hardened sandstone to resist mushiness or even used untreated is not that much of an issue except for the problem of turning to mush or not.
Cheers,