Simply not true. Compare the cost of a beer in, say, Thailand and Norway. Are you suggesting if the exchange rate were fixed they would reach parity over time?
The Big Mac index is better for many reasons, one being Mcdonalds is large enough to mostly optimize everything wherever they operate:
Sometimes the economics do conveniently work out this way, which is why some people might get confused. For example I lived in Poland for a few years, and at the time a dollar got you about three zloty, and for the majority of day-to-day stuff you did indeed have about 3x the buying power. Of course for things like computers you ironically had about 1/3 the buying power.
So in this case 60x is a reasonable assumption except not including the Purchasing Power Parity.
Zimbabwe is printing trillion-dollar bills, so everybody there must be rich....
Why is this relevant?
I find the vast majority of people are tripped up by currency conversion, but I'm surprised to find this on HN. In Japan $1 = 100 yen, but certainly I don't feel I have 100x in buying power. A bowl of ramen will cost me $8 in SF; an equivalent bowl will cost me 800 JPY in tokyo.
Let's not even get started on the Korean Won...