No, you are not being unreasonable.
They are being stupid. You offered to pay the fine, what more do they want?
Perhaps a note or call saying that you are confused to learn that they are annoyed, since when this happened, you offered to pay the fine and they said no.
Or perhaps they were expecting that stupid stupid thing people do
we'll pay
no, it's alright
no, I insist
Wouldn't dream of it, old chap
No no, you really must let me
not at all, it's fine
No, you have to.
oh well, ok then, you twisted my arm
but instead, you did
we'll pay
no, it's alright
oh, ok then
See, people are weird and they almost never say what they mean.