The IRS will generally take the most effective tack it can in getting the money it is owed. For honest mistakes, that usually means sending you a formal notice that it believes you are out of compliance and requesting that you pay them. If you pay them, all is forgiven. If you can show to their satisfaction, with supporting documentation, that you don't actually owe the money, all is forgiven. (I once got a notice that I owed $11K because of some stock sales I'd forgotten to report and education credits they didn't believe I was entitled to; after producing documentation on the cost basis of these sales, a course transcript from the educational institution, and an amended tax return, the total was reduced to $50, I enclosed a check for that, and I got a notice back that the matter was closed.) If you try to pull any funny business or argue with them and your arguments are not backed up in fact, they will viciously hound you until you pay the money that you owe.
If you pay them, they go away. Or sometimes they pay you and go away. (My first IRS letter was after my first semester of college, which was a bit disturbing since my whole income that previous year was ~$1k, but opening it revealed that I had neglected some sort of new education credit and they were giving me a small check to account for it.) My only remaining "fear" of the IRS is the scary Audit, because I know my record keeping is terrible and I don't want the anxiety of calling places and hunting down receipts or getting sworn letters from people that such-and-such checks were used for rent sharing not income/paying for services, and so I only hope that any audit could just be resolved by paying a lump sum even if with a bunch of effort that could get reduced...
I don't believe I've ever heard of someone being charged with perjury for signing an IRS document that wasn't true
You could look for some perjury charges if you disbelieve.
Citation needed. The IRS can be among the most vicious of any federal agency. Having dealt with FATCA situations with overseas Americans, Treasury is, in my experience, nobody’s friend.