I'm taking that dialogue as being dream sequence stuff, like when you dream you can jump and suddenly your taking strides athat are kilometers long, or you turn a corner and are on the next street, which in real life is in a different city. We already know that dream Summer doesn't talk with Nika honestly - the immersion gets broken when Nika realises things don't make sense.
If the cabin is 6 hours away, either Noji commutes for 6 hours to work at the hospital while they're in school, or Noji doesn't work at the hospital at that time, or the cabin is not in actual walking distance - it's just the way the dream worked, or they lived halfway between the cabin and Wollust. I don't remeber there being a sense of Noji having a different job before working at the hospital though, and it's a position requiring training. Noji talks about wishing she'd tried to start her own practice, but feels it's too late now - so I assume she got the job with the hospital as a career.
Also, the violent incident took Nika to the hospital - Nami mentions he's been there before. It's be strange not to take him to a closer hospital.
The timelines of when these things happen will help us make sense of it - we're still making guesses.