That whole hearing was exactly the textbook of cruel trilemma.

The fifth amendment was something created to prevent the situation that arose in 17th century England with being forced to take an ex officio oath. Putting them into a situation where:

• You either incriminate yourself to some crime
• Commit perjury by not sticking to a record that you may have forgotten
• Be held in contempt because your service bars silence

In Brown v. Walker (1896) the US created a case law that took the traditional meaning of the fifth to a new level that allowed twisting of it's words. In that case, anyone given an unconditional pardon could not self-incriminate, and since the fifth had (in their opinion) a requirement that protection only extended to self-incrimination, those with a pardon couldn't invoke the fifth for things they have been pardon for.

It is this that creates the new modern US cruel trilemma.

• You either say something that reveals in some manner a new crime not covered by the pardon
• You commit perjury by saying something in the record that is held to not match the record for which you were pardoned
• You are held in contempt because your pardon bars silence

That is what Fauci walked into. A situation where the legal technicalities had been so twisted that each of his rights both helped and hurt him. There was no correct answer since the deck had been stacked already. This is the same technicalities that were used back in the McCarthyism days. People wonder why people would willingly go to testify in front of the Senate and not just remain silent? Because the Senate had twisted the legal framework such that there were no options open to people.