That makes perfect sense. And by the same logic, if someone uploads or shares a movie that a distributor would have paid between $10-20 million for the rights to distribute, the fine should be about $50-150k.
It's important to remember that people aren't being sued for downloading, they're being sued for uploading. And distribution rights are expensive. Apple doesn't pay Warner Brothers $1, once, in exchange for being able to distribute some new song. AMC Theaters doesn't give New Line Cinemas a simple $14 for the rights to show Straight Outta Compton on a thousand screens for the next three months.
Remember back when Michael Jackson bought the distribution rights to the Beatles' catalog for several million? It worked out to around $20-30k per song... which happens to be right about the same amount Jammie Thomas and Joel Tenenbaum had to pay for their infringement.
I'm not sure if you don't understand the underlying economics of the movie industry, or if you don't understand how popcorn time works - or both. Companies don't pay a lump sum for "distribution rights". Using AMC Theatres as you did, the studio would be paid per ticket sold to see the show (basically the entire ticket price, with the venue making income on concession sales). So if a ticket is $8, and 10 people attend the movie, AMC pays New Line $80. If 1,000,000 people attend, AMC pays $8,000,000. Your theoretical example of a Hollywood studio only making $14 in theaters can and does happen. Here is a list of 11 movies that made less than $400 gross while they were in theaters - some staring actors you probably recognize: http://mentalfloss.com/article...
Popcorn time seeds the torrent while you are watching the movie. So if I watch a movie and "upload" 4% of it to 12 different people before it ends, I only "distributed" 48% of a single movie in total. Using our $8 ticket price, wouldn't I owe $3.80? I can't imagine it getting to $50,000 - $150,000 as you suggest. The only exception to this would be the one person who originally uploaded the movie to the internet... but that would be both off topic and contrary to your 'uploads' statement so I won't address it.