if I remember correctly, that's just how the át- is used. it means going over or through something, ending up on the other side.
"átmegyek az utcán" - "I am going through on the street" i.e. "I am crossing the street"
"átmegyek a parkon" - "I am going through on the park" i.e. "I am going through the park (and end up on the other side)"
"átmegyek a szobán" - "I am going through on the room" i.e. "I am going through the room (and come out the other side)"
I don't know whether there are examples where -át requires -ban/ben, but these are the examples I learned in another course.
and a duolingo example in this lesson that I came across just after answering here:
"A macska átnéz az ablakon" - "The cat is looking through on the window" i.e. "The cat is looking through the window"
I guess it's to separate "through" and "across" from "over", which is used as the english tranlation in all the cases where there is just a movement to the side "over to the other country" or "over to the other room" or "move over on the sofa". In these cases, there is no -on/en, because nothing is being crossed through like a street, a park or a window is in the examples above.
@any proficient Hungarian speaker: please confirm or deny. I just made up a nice hypothesis that explains the example sentences that I've seen, but don't know whether it's true or not
I gave what I thought would be the acceptable sentence: "The tourists walk over onto the street." And that was rejected (rightfully) in favor of the much better one above. Can't win! :)
One question: why is "utcán" in the (?) case. (Sorry, I don't remember the name, it's the one with on/en endings.) That would be "on the street" correct? How does that become "across the street"? I guess, literally, they would be walking across on the street?
Literally maybe. You probably know the answer to your own question by now. Some of these expressions are just associated with this (?) case. Maybe especially the preverb "át-", but others may do it, as well.
"Átlépek a lábadon" - I step over your foot.
"Átmegyek a szobán" - I walk/go across the room.
"Áthajtok a piroson" - I run a red light.
"Átkelek a zebrán" - I go across on the crosswalk.
"Kimegyek az ablakon (keresztül)" - I go out through the window.
In English (at least in NZ) there is a significant difference. "Street" is smaller and within a community, "Road" is often between communities. When you look at a street map for a city and see "roads" you can visualize how the city was once made up of lots of little places - linked by roads.
Also a "road" is often just the path. A "street" includes all that is on it.