Yeah the directions are a bit misleading. When they say to face it out they are assuming that you are either placing the boards on the inside of the structure or are going to cover it with siding.
I dont know what your weather is like where you live, but if it is a wet climate the OSB may/will start to come apart. In a dry climate it may last longer, but it will still start to come apart. The problem with just painting it is I would be afraid that moisture would build up under the foil and it will start to peel off. It will probably start to peel after a few good rains anyway and Im not too sure how well the paint will stick to the foil. OSB was not made to get wet it should always be covered. I never was one that liked to be the barrier of bad news, but OSB is OSB.
I know it might be a pain and a lot of extra work, but can you pull the boards off and turn them around? Well, then you would have the problem of the birds pecking at it, but they may not peck at it too much you never know. If you can turn the boards around then you could put a good coat of paint on the outside and that would give you time to afford some kind of siding to cover the OSB. The barrier will still work even faced to the inside. You could try wrapping it with something like roofing felt, just something to protect the OSB from getting too wet too often. That is the main thing about OSB - keep it as dry as you can.
As far as the coon proofing the small coop just make sure they cant dig under it if it has an open floor and make sure the open sides are chew proof. If it looks to you like a coon might be able to break into it, you can bet it can. Maybe someone on here with more coon experience can help you more with that question. Good luck to you with your chickens. Sorry for the bad news about the large coop.