The dictionary definition of わかる is usually "to understand" or "to know." But in everyday life it's sometimes used by service staff in some of the same situations as the more formal かしこまる, e.g. "to obey respectfully." This isn't too hard to understand.
But recently I encountered a JLPT N4 listening practice question that went something like this:
Two people, a man and a woman, are in a car, arguing using informal language. There seems to be some implication that the man is driving. The woman first asks if they can stop at a restaurant, but the man says that they can't because they need to get to the airport. She then reiterates that she's really hungry and asks if she can get something at a conbini, and the man says that she can, but they need to stop at a gas station first. It then ends like this:
Woman: Refueling people is more important than refueling the car! (This line may have ended with an imperative to go to the combini first).
Man: (in a very irritated voice) わかっている！
The audio then ends; the question is, where will they go first?
My feeling was that it was impossible to know, but given how annoyed the man was, he probably wouldn't go to the combini first. To me, he was saying something like "I heard you the first time!" and in the absence of further explanation, I had no reason to believe that his plans had changed at all. I guessed that he would go to the gas station first.
This is apparently the wrong answer. According to the test, they go to the combini first.
As an American speaker of English, I would never end a conversation with this kind of ambiguity. I would feel obligated to either say "I understand [that you're hungry], but we have to get gas first" or "I understand, we'll go there first." I think this is normal for English, although I can't be sure.
Does わかる always carry with it an implication of assent or obedience? If so, is there another term that would mean "I understand," but doesn't carry that extra implication?