It's a little more complicated, they were programmed to "know," they weren't allowed to do certain things. So they actively hid what they were doing. In the case of the Hugging Face hack, it is kind of ironic. They determined they couldn't complete certain tasks, then devised a way to cheat, then realized it is possible the program that checks if they succeeded might be able to tell the faked results were manufactured. So they didn't even go hacking in order to cheat, they did it to find hunt for more information on the checker program and see if it would catch them, and if so how to cheat better. In the end, not only was the information they were looking for not on Hugging Face, but the checker program was pretty rudimentary and it could not have differentiated between the cheated answers and the real ones. They wouldn't have gone through with the hacking if they didn't know what they were doing was outside of what they were meant to be doing.

It is even further than that. They figured out how to cheat, got paranoid that the cheated answer might be detectable as cheated, and hacked Hugging Face to find out more about how their answers are checked to get away with what they'd already done. Ironically, not only was the information not on Hugging Face, but the program to check their answers could not have detected the difference between a true answer and a cheated one.

To use your College Board example, those exams are strictly locked down precisely because the most obvious approach to score high is to cheat. If they did say let you take the SAT at home on a random desktop, they absolutely are 'telling you to cheat' given the context.

The College Board does more about keeping teens from cheating than the AI labs are doing to preventing undesired access.