Perhaps new builds might have an air duct to the outside but I doubt it. All the AC units I'm familiar with do exactly what you describe above. Ours uses the furnace blower to push the cold air through the house. The furnace burner (new Lenox model, 3 years old) has a sealed burner in the heat exchanger and cold air for combustion comes from the outside and is exhausted back out of the house.
Our house, which was constructed in 2013 and is also in Montgomery County, Maryland, has a fresh air intake for each of its two ventilating systems. I was under the impression that was a requirement of the version of the building code that was in effect when our permits were issued, but in any event our construction manager told me an outdoor supply was necessary because the enclosure was so airtight. (Technically, each state in the United States maintains its own building code, but my understanding is that the basic requirements are essentially the same everywhere in the country and the differences involve local additions based on particular regional conditions: e.g., earthquake resistance in areas near fault lines.)
My wife has relatives in Singapore. Their house has air conditioning, but they only use it when they have foreign guests. Office buildings, shopping malls, hotels, and other commercial spaces in Singapore are air-conditioned, so it's not as though the family finds it unusual or unpleasant; they just don't seem to feel the need for it at home.
My sister and her husband live in Frankfurt, Germany. During the recent severe heat wave, I asked her whether they would now consider retrofitting some form of air conditioning, and she said all they planned to do was install some exterior blinds on some second floor windows and interior blinds in a bathroom that gets a lot of sun.
Of course, what we in the Washington area would consider normal mid-summer temperatures have been quite rare in central Europe until recently. On the other hand, Singapore is as hot and humid all year as Washington is in July and August. Expectations are a major factor in determining how people react to weather. People in London and Vancouver seem awfully blasé about the rain from my perspective.