If I were to guess, my guess would be that it's a good idea for an interpreter to be perfectly level-headed and stress-free to accurately understand the patient, understand the staff, and do the interpretation, and the stressful situation could potentially mean that a family member would be distracted and might miss things. It's an assumption, to say that someone might not be capable of translating under the circumstances, but it's one that's aimed in a direction of less danger to the patient.

It's only a guess, though.