A good question, and yes, you are correct. A few things to understand:
The Entry Reciprocity Fee is ONLY charged at SCL. It applies (differently) to citizens of Albania, Australia, Canada, the United States, and Mexico.
Other citizens don’t have to pay. (Yay for the Kiwi passport!)
The receipt for payment of the reciprocity fee is attached to your passport. On subsequent visits to Chile, you don’t have to pay the fee again for the life of your passport. When you get a new passport, you’ll have to pay the fee again.
Source: I have found several sources of travellers who have done this and written about it, as well as asking a US friend who has done it a couple of times.
Credit:stackoverflow.com‘