Not necessarily. With federal courts having ruled a person can be tried twice for the same offense - in federal court and again in state court - he could refuse to testify because a federal pardon does not protect him from state court charges - meaning he still can take the 5th.
I also wonder how these people charged with lying can be so stupid to not simply always answer "I don't really remember exactly, I think this might be correct but I'm not sure since in my life I've spoke to about a million people and seen a few million pages of papers..." and then end any statement with "I'm not really sure about that, though. Maybe that's accurate, but I could have this mixed up with something else."
I recall being in a deposition for which my goal was to not be locked down on anything nor reveal anything. My answers were LONG, I would often just ramble on and on, but also endless qualifiers like above. After 5 hours they gave up - and settled the lawsuit on behalf the buddy I was a witness for. Not actually answering any question with any specifics or certainty is a piece of cake for anyone with an IQ over 80. Even the most simple questions are easy to avoid answering.
For example, it certainly would be easy to prove I have posted on this forum. However, getting me to acknowledge that under oath in questions would be impossible if I didn't want to answer. "I've been on and off forums for decades and there are so many. I probably have posted thousands or hundreds of thousands of messages maybe and read millions. But which one for sure? I'm not really certain. The ID you showed me looks familiar, but I usually set any login and passwords to automatically be entered, so maybe that's me, maybe not, I'm not really 100% sure."
Another example is if shown some document and asking "is that your signature and is this the actual document?" Answer: "I'm not a handwriting expert and I scribble my signatures that anyone could do. I certainly don't memorize things I read or sign, so I can't say for sure if that is my signature and certainly can't say whether or not this is the actual document or if it was rewritten by someone changing what it says..." etc.
I'm stunned at how foolish these people are to let themselves get trapped in perjury traps.