I'm not 100% certain, but I think that only applies to the accused defendant in a criminal trial; I don't think it would hold true in a civil action.
Although I only ever rely on “Law and Order” and am loath to cite “Wikipedia”, counselor Wiki advises:
“Giving testimony in a trial or other legal proceeding that could subject one to criminal prosecution.
The right against self-incrimination forbids the government from compelling any person to give testimonial evidence that would likely incriminate him during a subsequent criminal case. This right enables a defendant to refuse to testify at a criminal trial and “privileges him not to answer official questions put to him in any other proceeding, civil or criminal, formal or informal, where the answers might incriminate him in future criminal proceedings” (Lefkowitz v. Turley, 414 U.S. 70, 94 S. Ct. 316, 38 L. Ed. 2d 274 [1973]).
But I still find it amazing that a person in that position would give an interview on these factual issues — for example, without even having any connection between Dr. Hatfill and the park.