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?