What is the spelt-out form of Mike Huckabee’s message, “(He) would not have received [permission] had they."

Time magazine’s (Jan 27) article titled, “Huck: “I didn’t approve that message,” begins with the following sentence:

“On Fox News' "Your World" Friday, ex-AR Guv says Gingrich's campaign did not ask to use his sound bite and "would not have received [permission] had they." Adds he would "love" for the Georgian's team to take down the ad.”

To a non-native English speaker who learned English mostly from “bookish” English readers, it is difficult to understand the phrase "would not have received [permission] had they," particularly the meaning of ‘had they.’

Is this grammatically perfect expression? If not, what word is omitted before ‘had they’? How can the phrase be spelt out in easier-to understand format?

Solution 1:

To fully spell out the phrase:

They did not ask permission to use the sound bite, and if they had asked for permission, they would not have received it.

The sentence is grammatical; "had they" is an alternative formation of "If they had". Similarly, "Were they" can be used in place of "If they were":

I said 'Yes' when they asked last week, but were they to ask today, I would say 'No'.

Solution 2:

The omitted, implied word is "had they asked".

Solution 3:

“(He) would not have received [permission] had they."

Is better put as "“(He) would not have received [permission] if they had."

hope this helps :-)