I have always taught my pupils that crossing meant going across something, as in "I crossed the street", This sentence means that I walked across the street from one side to the other.
I do not think I have ever used or accepted crossing through anything. If you traverse a strait, canal or street longitudinally you go along, down, up or through it.
The trouble with news broadcasts of any kind is that they are made at short notice, obviously, as otherwise they would hardly contain News, would they?
This means that those who draft them, write telepromts, etc. need to be good at the language they are writing. Then too, there are well- defined limits to how many words anyone can read, take in, and express from a telepromt, so the message has to be concise.