I think I know what you mean by cornering; in this case, trying the 4 along the bottom row starting from each corner, to enable you to narrow it down sufficiently to make progress. And I did it! But I would consider it a fairly standard tool for solving hanjie puzzles.
Velma's explanation is what many people on this site call "2-D logic". That's how I did it too. No idea what "cornering" is, but would be very interested in knowing!
Yes, the puzzle is symmetrical, but entirely possible without assuming this (I always first try to see if puzzles are possible without making any assumptions whatsoever).