Does swearing in these witnesses make any real difference? Per 18 USC 1001, it is a crime to make a materially false representation in any matter within the jurisdiction of the legislative branch, regardless of whether the person has been sworn in. Is there some other reason it would matter?
I'm not sure. Is that the section most contempt/perjury charges related to congressional appearances are prosecuted? It seems like there is some significance if not swearing in, unless the demand is just political.
You're right: The perjury statute does require an oath. 18 USC 1621(1). But 1001 also seems to apply. Here's a case in which both were charged: perjury for false testimony to a congressional committee and 1001 for false written submission. Nothing in 1001 says it's limited to writing, though.
It's possible members of Congress just aren't aware of 10001 as much or perjury is easier to message politically.
Just realized that the 1996 amendment to 1001 substantially limits its application to false statements to the legislature. It only applies in "administrative matters" or "any investigation or review." If a hearing does not fall into those categories, then the lack of an oath would matter.