I think this thread (and everything I've read on this topic in the last few years) proves that people largely don't agree on the definitions of these terms, but having known many people who consider themselves introverted, "dealing with a lot of people superficially", and "dealing with near continuous rejection or indifference" is extremely poorly aligned with their personalities. Speaking personally, those things are my nightmare.
I can deal with rejection and indifference because I don't give a crap about the people on the other end of the transaction. It seems to me that you are describing social anxiety more than introversion. However, that was kind of the point of your comment that not everyone seems to agree on the definition.
I think, however, we are also dealing with understanding the word "superficial" differently. Superficial interactions with people in the sense of meaningless small talk of no consequence is more of an extrovert thing, I agree. However, when I said "superficial," I meant that you aren't really dealing with people at all, but rather hands from which you take money and into which you insert popcorn. There is very little real human interaction in that scenario even if you are technically around people all day.
EDIT: And in the door-to-door salesman scenario (which, I agree, sounds like hell), you are still spending the vast majority of your time alone in your own head walking from house to house.
If you're aiming to deliver a new pitch in 15 seconds time you're not really alone in your own head, especially not if you're scanning the garden for hints and clues that might help you make small talk that stops that conversation from coming to a quick end. But of course, if you like being alone in your own head, nobody's stopping you from not knocking on those doors...
Agreed, introverted people can probably cope with selling popcorn on autopilot surprisingly easily if they don't have related issues with crowds or self-confidence. But is running round a stadium shouting at people the first thing the average teenage introvert thinks of as a fun way to make money, even in a pre-internet age?