Yes, they need to send someone to one of a number of possible government offices. They'll have to show a reason for inviting a foreigner, do paperwork, and pay fees.
Going to the provincial capital is not necessary, but it is entirely possible that a small town wouldn't have the right office.
If you'll permit me a gross over-generalization, this won't be trouble to them, per se. Nobody likes it, but having to go to government offices and wait in lines is a fact of life in China. They're pretty accommodated to it. From my experience - though I haven't filed one of these forms - it's generally several hours to half a working day at a minimum, depending on what you're doing and how busy it is (it's never empty). In some cases it's possible to make an appointment ahead of time, but this only mildly ameliorates the waiting.