I wonder why when using the ref walking, the cell names returned empty strings, but when using GetInCell, all was good?
That is because the cell name is empty for the Tamriel exterior cells (exterior cells don't have names, so functions like GetName and %n return the worldspace name for them. It just happens that the Tamriel worldspace does not have a name, so Tamriel exterior cells have no name)
On the other hand, GetInCell checks against the cell EditorID (not the name), and all cells have an EditorID (well . . . not counting the 'wilderness' cells).
As for the WIKI text, what it means is that GetInCell will only accept an interior cell EditorID as a parameter, not an exterior EditorID. So, GetInCell will compile if you use 'AnvilTheFocsle' (interior) as argument, but will not compile if you use, for example, 'AnvilBay' (exterior).
This is why, btw, the game has dummy cells named Anvil (or Bravil, or Bruma), so you can use Anvil as argument for GetInCell and get a positive return for all interiors that start with Anvil and all exterior cells in the AnvilWorld worldspace (which, btw, as opposed to Tamriel, does have a name that, obviously, is "Anvil")
Oh . . . and I do not understand why you attempted to use ref walking to get the cell name