No, a UUID can't be guaranteed to be unique. A UUID is just a 128-bit random number. When my computer generates a UUID, there's no practical way it can prevent your computer or any other device in the universe from generating that same UUID at some time in the future.
It may not be likely that any two UUIDs will be the same, but they can be.
In this case, the code assigning UUIDs to devices may check a new UUID against any existing UUIDs already assigned to devices and throw away duplicates, guaranteeing uniqueness that way.
When a new disk is installed to a system, the usual practice is for a technician to define the partitions thereon. Labels are not unique and are not used. In the definition process, a software algorithm creates a UUID.
As the system already has a list of existing mounted UUIDs, the process of defining the partition automatically creates a unique UUID value. The new UUID value filtered against the existing list of mounted UUID's so as to avoid duplication. With partition creation,on the host system that UUID coupled with the partition number form a unique combination.
Yes really. Duplication could occur if the disk is prepared on system A for use on an existing system B.