This is interesting, because at the top of your note is says clearly that you "might" be entitled to a TWOV.

However, the airline has to make a call on this before you get on the plane in the US. If you are denied entry, they will be on the hook for a penalty which I believe is £2,000 plus detention and repatriation costs.

So a gate agent in the US has to second guess what the immigration officer is going to say. I wouldn't be trying this myself - you have to admit it does look like a rather dubious strategy!