That's completely different. Pleading the 5th and not testifying is completely different from giving false testimony - which is never protected. Even in a trial, if you are asked under oath if you handled the body, you are allowed to say that you invoke your 5th amendment rights not to respond; but you are not allowed to say "no, I didn't" if in fact you did (you can later be accused of perjury in addition to your conviction).