Nixon did not have an inside voice. He did, however, have a voice inside him.
The voice was a stowaway. The stowaway was a bird - specifically, a nuthatch. It was a nut with its hatch ajar. "Крыша поехала," say the Russians. "There goes the roof," they say.
The voice was a bottle inside a ship. The ship was wrecked by the pointy elbows of homesickness.
When it came to logic, Nixon was a one-hit wonder, a nonsense-prince.