Who told your brother that? It could not have been a doctor. In all probability and as stated by others above, ALS will eventually impair a PALS ability to balance but only once the muscles involved in balance are affected.
According to Wikipedia:
"Balancing requires concurrent processing of inputs from multiple senses, including equilibrioception (from the vestibular system), vision, and perception of pressure and proprioception (from the somatosensory system), while the motor system simultaneously controls muscle actions. The senses must detect changes of body position with respect to the base, regardless of whether the body moves or the base moves."
ALS only impacts one of these components of balance, namely the motor system controlling muscles. If the muscles involved in balancing on one leg are not affected by ALS, then you will still be able to balance on one leg. If your leg muscles are affected then chances are that your ability to balance on one leg will also be impaired.
Six years in, my legs are still good and I have not lost the ability to balance. I open drawers, turn on the shower faucet, flush the toilet all while balancing on one leg. Of course I will in all likelihood lose this ability once ALS progresses to my legs.