Just for the record, I was at the Llao Llao in Bariloche this weekend and they were exempting foreigners from the VAT. I didn't ask much as I am a local, but a pax from Brazil I met at the bar told me he was informed by the staff his stay would be cheaper because his original booking included VAT.

Since the Llao Llao in Bariloche and the Alvear in Buenos Aires are owned by the same group, I assume they must be doing the same at the Alvear.