I don't think it's realistic to keep checking this with immigration every month unless you have nothing better to do or really like the new immigration office (they do have AC and free water). My understanding is the same as
@Ba***
's, they only need it if you come back from abroad, not within Thailand. That's what I do.
If they change their mind the fine is a maximum of 1,600B, not exactly huge. And I'm sure word will get out when the first person is fined for going across the border to Lamphun, we will hear about it.