Permitting involves things like making sure the design is up to fire codes (eg there are setback requirements to make sure a firefighter can put a ladder on the roof) and the interconnection work with the utility that lets you send energy back into the grid. In the worst states, these extra costs are largely artificial barriers (ie outright anti-competitive tactics).
I believe Germany for example spent a lot of work streamlining these all these permitting and interconnection fees, and as a result has much lower solar costs.
What this company appeared to have proposed in this contest is that by bolting solar onto pre-fab homes in the factory:
1. Installation costs drop, presumably because it's built into the design of the home and there's factory tooling around it instead of a retrofit system; and
2. Permitting costs go down because the design is standardized and presumably you can get economies-of-scale if you're connecting a whole subdivision or trailer park all at once.
This also nicely addresses the equity angle since prefab homes are generally aimed at lower income levels -- the claim here is that this building can drop the price of solar by almost half for this demographic.
I'm not aware of having to notify the local council or power company about installing solar (you do have to get certification before you can receive money for generation though, but I don't think that costs significant money, its more a case of proving provenance of solar panels and equipment. )