In the narrow sense of independent individuals/states, you are correct. A country does not have a responsibility to run foreign aid programs. However, once you do, you enter into a agreement that involves some responsibility because now others are relying on you to fulfill your commitment.
Put simply, say you want to climb up a ladder and need someone to help, say, keep their finger on a button that prevents the ladder from toppling over. I have no responsibility to help you. However, to be nice I agree to help you. I press the button down and you climb up. Now say I change my mind and I want to go do something else. I now have a responsibility to tell you so you can safely come down and find another solution. What the US is doing now is shouting up at you while you're on the ladder and saying "hey, I changed my mind. Sorry, but I actually have no responsibility to help you out"