Indeed, Mr. Chair, you are quite correct.
It does not matter whether a witness is sworn in before a parliamentary committee or makes a solemn affirmation. In either case, the witness is bound to tell the truth when appearing before the committee. The only thing that may affect the swearing in is this: if a committee has proof that a witness lied, it could refer the case to the House, which could then decide to waive the protection granted the witness under parliamentary privilege. The removal of that protection could then open the way to a perjury charge being laid against the witness. That being said, this has never happened in 150 years.
In summary, Mr. Chair, a witness must tell the truth, whether he is sworn in or not. If he is sworn in, however, committing perjury could have serious legal consequences.