Is it possible to get the huntington gene even though there's no family history of the disease?

Yes: Huntington disease is autosomal dominant, meaning that affected individuals have one normal and one abnormal gene. Offspring of an affected parent (like arlo guthrie) have a 50% chance to get the abnormal gene. The expanded trinucleotide repeat that constitutes the abnormal gene can develop as a new mutation without prior cases in the family.