Quote from james_bond_3rd:
This is totally groundless. Fifth amendment cannot be invoked simply because one might perjure oneself. "Self-incrimination" only applies to testimony of past actions, not the testimony itself.
But try to explain that to a liar who is about to be exposed... and worse, try to explain that to a klansman who don't want his klansmen and klanswomen to be punished even when they commit crimes.