I have lived in the US my whole life and I do not find that to be the case. It is true that "how are you?" has the double meaning of "<generic greeting>" and

I have lived in the US my whole life and I do not find that to be the case. It is true that "how are you?" has the double meaning of "<generic greeting>" and "really, how are you doing?" but the fact that it can mean the first does not mean that it cannot mean the second. You learn from context which meaning is intended. It is also not unusual to ask the question in mode 1 but not be flustered when someone responds in mode 2, especially if they are a friend. This may seem confusing, but there are lots of phrases in lots of languages that have shades of meaning depending on context, so it is not unique.