Can't speak for the Incheon City girl, but they probably weren't lying to her. Incheon city does administratively cover many of the western islands...

A way to get around that is to get specific - what 동 (dong / neighborhood) or 구 (gu / district) is that in? Which subway station is it nearest to? What's the exact address of the school (maps.google.com can take English or Korean)

As for the video, it's a compilation of horror stories. Nothing more and nothing less. That's happened to some English teachers, yes, and I'm not saying some of them couldn't happen to you... That said, you are coming into a different culture with different rules and different mindsets that even many of the locals don't like. Recognize that before getting on the plane.

Yes, I agree. Horrible Horrible experience.

Yes, I have heard some horror stories. That being said, which profession do you know that doesn't have a horror story or two especially when that profession takes you to a foreign country. My advices are first, research your school or hagwon and make sure it's in the right location for you. Second, try to learn the language because a little can go along way. Most of my friends say that the language barrier is the hardest obstacle to over come. lastly, stop complaining and go have fun because the experience is what you make of it. Korea is a wonderful country and a place where I feel completely safe night and day unlike most American cities.

I had a good enough first job, but when I moved on, I ended up with kids who were about 10 years younger than promised. I'm aware of Korean age vs. Western age, but toddlers are not to be confused with middle and high schoolers. I was told I'd get to teach more high level students, doing debate and test prep. I ended up doing ABCs and literally told that I'm to wipe a--es (which I refused). I quit early on, giving ample notice and being as helpful as any mere mortal could be in that situation.

Fast forward to next gig. It's an after school program. The apartment turned out to be unlivable. I ended up living first at a jjimjilbang (where I was sexually attacked), couch, goshiwon and different jjimjilbangs. I was promised a new place and after pushing the dates then threatening to fire me every time I asked, I just left.

If job 3 was my first, I would actively work to ensure that no one ever goes there. Job 2 was merely inconvenient in comparison even though that contract was full of lies.

Tips
1. First timers: go through GEPIK/SMOE and giant branches of giant hagwons. This doesn't mean you're going to have a good experience, but when it comes to fulfilling the promises of your contract, it's the best bet. Your co-teacher can be your best friend or your worst enemy, fluent or pretty much a novice, but most likely, s/he'll be somewhere in between on both counts. As for hagwons, the bigger the school, the easier it is to research. Big branches will generally mean you'll get some sort of mini-training and a bit of feedback on your performance. The exception would be WONDERLAND.
2. If you don't love young kids, don't do kindy. "Kindergarten" is age 3-5/6 Western age. Make sure you've spent a lot of time with kids in this age group before you agree to this sort of job. These gigs also involve longer hours as most involve hagwon after the kindy kids go home. Tolerating them is not enough. Make sure you love them or you'll hate your job.
3. If you have thin skin, reconsider. This isn't a good place for sensitive types as people may stare at you, actively avoid being close to you, point, laugh, gawk in horror, etc. If you insist on coming, try international schools or working with kids who've lived in the US. Live and work in Itaewon, and never leave. If you do this though, you completely miss the benefits of living in a foreign country.
4. If you're significantly overweight, not "traditional" looking, black, brown or tan really well, make sure to seek out the open, worldly people living nearby. For the sake of sanity.
5. Follow your gut when choosing. Don't agree when there are vague details. Find out the exact address, google the school and the address, ask to speak to current or former foreign teachers. Do your part. If your recruiter is being dismissive or excessively pushy, find someone else. Don't feel obligated or pressured to agree to anything you're not comfortable with fully. If it winds up being a disaster, it's hard to undo so choose carefully. Even if job prospects are bad where you are, finding yourself in one of those nightmare situations will be worse.