Final answer:
The statement is false because X inactivation is a random process, and there is no mechanism ensuring that the non-translocated X chromosome specifically becomes the Barr body in somatic cells of heterozygous women with a reciprocal translocation involving an autosome and the X chromosome.
Step-by-step explanation:
The statement that a woman who is heterozygous for a reciprocal translocation between X and an autosome would always have the normal, non-translocated X as a Barr body in her somatic cells is false. This assertion is incorrect because X inactivation is a random process in female mammals, including humans. When a female embryo is at a stage of just a few thousand cells, one of the two X chromosomes in each cell becomes inactivated and condenses into a Barr body.
This inactivation is random, and it does not preferentially affect the normal X chromosome over a translocated one. All daughter cells of that original cell will maintain the same inactivated X chromosome, which results in females having one active X chromosome in each cell, thus compensating for the dose difference between males and females.