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Pretty sure that is completely false, though it is popular to say. It 100% fails even a basic sniff test. The rate of energy transfer from outside to inside will be greatest when the inside is coolest, so the air conditioner will have to work harder overall to keep it that way.

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It can be true, but usually not for AC units, as these are quite effective at only heating/cooling the ambient air and not the walls, ceiling etc.

Regular heating can waste a lot of energy to heat the entire structure of the house, especially if you have thick walls, so it does more make sense to try and keep the temperature stable.

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