Clarifications of the exemption:
Not all lodging establishments can offer it as they must register with the tax authority to be able to offer it (and thus required to make a copy of the passport and tourist card of a tourist taking advantage of the exemption).
If registered to offer it, I understand it is not mandatory that the lodging establishment offer it to tourists.
There is an official time limit for tourists in Chile to be able to take advantage of it. A tourist that has been in Chile over 59 days is not eligible for the exemption though I'm sure many have slipped through the cracks (the problem will be for the lodging establishment if audited).