As you can see from the link provided above, it's not an "extra". It's simply the standard rate, and then there discounts only for Argentinians (and even deeper discounts for people in the state that the Iguaza Falls are in, Missiones, and no charge for people who live in the adjacent town), plus a lesser discount for people from three adjoining countries.

Everyone else in the world, not from Argentina, Brazil, Paraguay, or Uruguay, gets charged the same $100AR fee (for the first day), except for reductions for age and no charge for disabled.

So it's not that they check whether you're American. It's simply that if you don't prove you're from one of those 4 local countries, you automatically have the "rest of the world" rate.

Now, it's still unclear from that website what happens for day 2 and beyond. First, they say you get a "bonus" (meaning a discount, I'm sure) for day 2, if you leave on day 1. But those staying at the Sheraton don't leave on day 1 (since they stay inside the park by staying inside the hotel for the night). Furthermore, the site doesn't explain what happens on day 3, and seems to think that "one day is not enough" but two days is the most you'll ever need. In the past (per tour books, which have obviously not been updated for this 2011 price change) it was apparently no extra charge for day 3 and beyond. (Which is a bit similar to US Nat'l Parks, which typically charge once and then that admission is actually good for up to 7 consecutive days.)

So I guess only someone who's stayed multiple days since this 2011 price change went into effect can explain how this works (after your first day admission) if you stay at the Sheraton multiple days. And even then, it might be different depending on whether you leave the park during your stay or not?

Btw, per xe.com, as of today, 100.00 ARS = 24.3754 USD. So that's in line with the bigger US Nat'l Parks which may charge $25 for a visit (although like I said they typically then don't charge again for the next 6 days).