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Update: 

I just found the following text on the IRS website on page 1 under General Instructions (I put the link in the "who must file" heading). I think I will go by this and just not include the K-3. Hopefully, it will be the right call.

 

Who Must File

The S corporation need not complete these schedules if the S corporation does not have items of international tax

relevance (typically, international activities). Any S corporation that is required to file Form 1120-S and that has items relevant to the determination of the U.S. tax or reporting obligations of its shareholders under the international provisions of the Internal Revenue Code must complete the relevant parts of Schedules K-2 and K-3. See each part and section for a more detailed description of who must file each part and section.