They do mostly. The only parts supplied from outside are those that are supplied to other car manufacturers too, such as ABS units, radiators or air/con systems. Many of the electronics are supplied by Jap manufacturers, that also make them for other Jap car builders, but not really anywhere else. Mainly parts that don't have to be unique to Honda.
They have only ever twice used engines not manufactured by themselves, and that will end with the next model Civic.
Tell me where you'd by a pattern boxed 'Toyo' or 'Keihin' radiator?
On the last model Civic, them ones they shared with Rover, they definitely did use locally manufactured parts, and some where available at factors - brakes and such like. However, even now they are starting to remanufacture these parts in-house.
So, even where Honda don't actually make a part themselves, they are being made specifically for Honda, and nobody else.