No, I don`t think you are wrong--any aircraft squawking 7700 is usually a full emergency, but it can be any number of things, from a tech fault, ill /disruptive / passengers or even crew.
I am sure their are others on here that can give better insight, I would think if it`s a really big problem, then nearest suitable airfield would do just fine.
Other considerations could be related to the paperwork involved, and if an airline has any sort of arrangement with particular airports / ground handling agents.