If this is only about the AIC rating, then you are correct; the rating is based on the voltage that it is being USED FOR.
You also however used the term "bracing" which is different. Bracing or bus bars is the same regardless of voltage. So if you put a breaker rated for 65kAIC into a bus system that was braced for 22kA, the system could not have an SCCR of greater than 22kA. I don't know if that's the case here or not without data on the ATS, I'm just pointing out the semantics issue here.
IC = Interrupting Capacity (in Amps, hence AIC) of an interrupting device, like a circuit breaker or fuse. This is the maximum mechanical forces that the device can safely handle, and the forces are based on ENERGY, not just current, hence the current capability going up as the voltage goes down.
Bracing = the mechanical strength of bus bar supports or other current carrying components to handle the magnetic attraction and repulsion forces that take place during a fault UNTIL the interrupting device clears it. Because it is based on magnetics, it is only related to current, not voltage.
Short Circuit Current Rating (SCCR) = the total current that a device or system can safely handle during a fault event, basically a combination of the IC of any interrupting device AND the bracing of any current carrying components. This is what we used to call the "Withstand Rating" and can be affected by the "let-through" current of any current limiting devices that are part of the system or up stream of it, so long as it was TESTED AND LISTED that way.