What on Earth does "cheap at half the price" mean?

There has been a saying in American English: "Cheap at twice the price." This has traditionally been used to indicate that something is a great bargain.

"Cheap at half the price" is a humorous reversal of this statement. It is used to express contempt for the quality or price of an item, or both.

From http://www.phrases.org.uk/meanings/cheap-at-half-the%20-price.html:

Those, who suffer from literalism, faced with an item offered at half the usual price would expect it to be cheap - what isn't cheap if you halve its price? 'Cheap at twice the price', now there is a bargain.

The interpretation of this phrase has caused some debate.

(in Phrasefinder Bulletin Board):

1. 'Cheap at half the price' is understood to mean 'reasonably priced' and if people understand that meaning why worry about logical niceties?
2. It was never intended to be taken seriously and is a pun on the meaningful phrase 'cheap at twice the price', intended either humorously or in order to deceive.
3. It is just an error made by people who meant to say 'cheap at twice the price' but didn't think hard enough about what they were saying.

I have always assumed that it was short for "It would be cheap at half the price." Of course, this doesn't make any sense literally. But it could have started out being used ironically, as a twist on cheap at twice the price, and at some point the meaning was reversed. A Google Ngram doesn't tell us much.

Cheap at twice the price has been around since 1853.

It sounds like it's used ironically.

The iPad is cheap at half the price

Meaning that the item isn't cheap at all, but it would be if it were half the price.

But, apparently there is some deep-rooted debate going on about this.

Phrases.org lists the same explanation I do, along with some background and other interpretations.