That is correct.
Including the edited-in bit about in-faction supply: you don't pay for the supply your colonies need, but if your colonies can get their supplies from in-faction sources, that reduces maintenance costs of industries and structures planet-wide, up to a theoretical maximum of 50% cost reduction. (In practice, you will usually not get to quite the cap, due to certain commodities being illegal - while you can turn on that free trade toggle, it will attract hostile expeditions from certain factions if it's on for a colony larger than size three.)
...That said, there's some background simulation of trade fleets, and at irregular intervals you'll get supply interruption events, cutting availability of materials to what your colony needs minus two*. There is nothing you can do to prevent these. The best you can do is to minimize their impact when they happen via vertical integration, i.e., having Refining on the same planet as your Heavy Industry so that you can't get an interruption to metals / transplutonics, only their corresponding ores.
* This is an important distinction, because if you have, say, a demand of five organics, and you get hit with a supply interruption reducing the available supply to three, you cannot partially mitigate that via temporarily installing an AI core - the AI core will reduce demand to four, and your supply will suddenly drop to two.
