Well, it's obviously true that it's not a step function. But the slope is really steep. Someone with just a tiny bit of equity can sell their home and walk away without having to pay anything. Someone with just a tiny bit of unsecured debt who wants to move loses almost nothing (a beaten credit rating for someone with income isn't nearly as serious as you think) by walking away, and saves thousands of dollars in fees (typical real estate fees in the US are 5/6%, and paid by the seller!). That may not be "binary", but it's pretty close.

The real determining factor in your case, I suspect, isn't financial but one of convenience. Finding a new home is a hassle, and you don't want to bother with it. It makes more sense to stay where you are because moving doesn't get you anything but grief. But if you got a great job in a different city, would you really be seriously thinking about trying to sell your underwater house?