In fact I typically don't take the $92k foreign income exclusion, because excluded income isn't eligible for IRA contributions, and I'd like to keep contributing to an American IRA. So I report my full Danish income on the 1040, then subtract the Danish taxes, and end up owing $0 without even using the exclusion at all.
Such treaties exist with 24 countries, so of course you'd be right if I didn't live/work in one of those 24: http://www.ssa.gov/international/agreements_overview.html