Yes it's true, although I haven't tried it yet! There are some temples in the city and also countryside where you can go and sleep and as far as I know you are provided with meals as well, but it can cost a bit of money!
A friend of mine back from her travel in Korea. She did stay here in temple, and she said it was quite good experience. She recommended that I should stay somewhere in the rural site, there would be more relax, and clam :)