IRS has issued notices in specific cases (to qualify nonfilers for Section 6428 series refunds) allowing interest of $1 to be reported, to trick the system. I would take this as a warning that it should not be done in cases where not specifically permitted.

How difficult is it to reduce the amount of the foreign earned income exclusion by a few dollars so that there is positive AGI, but no tax? I am reminded of the case of a public figure who reduced an allowable credit or deduction so that the return would show $750 tax, when none was actually owed.