Yes, they absolutely and literally are. Saying they do not expect payment when they do is a lie.
No it is not. A lie is a deception. This is not a deception. This is a ritual, where they are broadly speaking showing hospitality/lack of greed by refusing and you are showing respect and honour by insisting. That's what it means. Meaning is not always literal interpretation of words. Meaning is what people understand by those words. And what they understand by those words is not any kind of deception.
Let's try an example in English.
If you ask a British person how they are and they reply "not too bad", they are telling you that they are engaging in the ritual and acknowledge your question (and thank you for it), but will not otherwise divulge details. The answer covers everything from "stuck in the trenches of WWI" to "won the lottery". They are not deceiving you into thinking they are merely in a literal sense not doing excessively poorly.
Just because you personally don't understand the meaning does not mean it's a lie.
You are pretending words don't have their meanings for the sake of making an argument yourself.
You're pretending you can deduce meaning from the literal dictionary definition of words. This is not true, because idioms exist.