Something is missing here. If you say you are a permanent resident of Colombia, you should either carry a Colombian passport, or a resident's visa in your US passport. If you have two passports, you travel TO Colombia with Colombian passport, and travel TO the USA with your USA passport and it would not be a problem. Did you show them proof that you were a Colombian resident?
As for your statement "it would be my problem not theirs" is inaccurate. If Colombian immigration requires that you leave the country within 90 days unless you have a visa, YOU must be able to prove that you have transportation to leave the country within that period. Airlines are subject to huge fines, thousands of dollars, plus deportation expenses, for every passenger they board who is not properly documented.
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