Chiefly used in the simple past tense or in the perfect tense and preceded by just, the U.S. phrase to fall off the turnip truck means to be naive, ignorant or gullible.

The image is of a country person who has just arrived in town on a turnip truck.

The phrase in use—In the 2012 thriller film Taken 2, there is the following dialogue between Lenore (Famke Janssen) and her ex-husband, Bryan (Liam Neeson), when they are going out for lunch in Istanbul; their daughter, Kim (Maggie Grace), has decided to stay at the hotel on the pretext that “jet lag just hit” her:

– Lenore: “She thinks we just fell off the turnip truck.”
– Bryan: “What do you mean?”
– Lenore: “She’s trying to play Cupid.”
– Bryan: “Oh, I see.”

These are the earliest occurrences of the phrase that I have found, in chronological order:

1-: From Whatshisname Advises Ford, by Merrill Lockhard, published in the Nashua Telegraph (Nashua, New Hampshire) of Wednesday 16^th July 1975:

State Republican Party boss Gerald Carmen was to meet yesterday with campaign aides of President Gerald Ford ¹ to convince them that Mr. Ford should not be a candidate in New Hampshire’s first-in-the-nation presidential primary on March 2, 1976.
I don’t know exactly what the conversation between Carmen, a Manchester tire dealer, and the aides was like, but I suggest it might have gone this way:
[…]
“[…] I’m here to recommend that Mr. Ford . . .”
“Recommend? We don’t even recommend to the President. He gets enough recommendations from Congress. He can’t stand any more recommendations. We don’t get paid to do that. What did you do, just fall off a turnip truck?”

¹ The Republican statesman Gerald Ford (1913-2006) was the 38^th President of the USA from 1974 to 1977.

2-: From an article by Kirk Bohls, published in The Austin American-Statesman (Austin, Texas) of Friday 8^th August 1975—Yogi Berra ² had just been dismissed from his post as the manager of the New York Mets:

The Mets, before Yogi’s firing, were 9½ games behind Pittsburgh but Berra never once said, “I couldn’t have done it without the players.”
But modesty wasn’t the reason he didn’t say it. Common sense was. Anybody who thinks a manager has ever won the World Series must have just fallen off the turnip truck. No manager ever stole 118 bases in a year, pitched a no-hitter or hit a winning home run.

² Lawrence Peter ‘Yogi’ Berra (1925-2015) was a U.S. baseball player, manager and coach.

3-: From a letter by one Mrs. Celesta A. Deter, published in the La Mirada Review (Whittier, California) of Thursday 2^nd October 1975:

On Monday night, Sept. 22, I spoke-out at (an East Whittier City School District) Board of Education meeting. […]
Wednesday evening articles appeared in both the Daily News and the Review. The articles were identical, except, that in the Review at the end of the paragraph that related my views and those of (Todd) McIntosh, (another parent in the district), there was a little statement in parenthesis. The statement said that (district Superintendent Keith) Walton disclosed Tuesday that both Mr. McIntosh and I are married to teachers in the district.
Now, none of us are children and we did not “just fall off the turnip truck.” This is what is known in journalism as a “loaded” statement. The intent of course is to discredit anything we may have said.

4-: From the column Chamber Chatter, by Vivian Weer, published in the Cloverdale Reveille (Cloverdale, California) of Thursday 2^nd October 1975—the following is from the account of festivities organised by the Cloverdale Chamber of Commerce:

While the cooks and servants were outstanding, we just can’t overlook our clean-up committee, which turned out to be most imaginative! (Our Directors didn’t just fall off the turnip truck, you know…).

5-: From the column The Lighter Side, by Dick West, published in several U.S. newspapers in November 1975—for example in the Martinsville Daily Reporter (Martinsville, Indiana) of Friday the 7^th:

I went to a dinner party the other evening at the pad of a trendy bachelor, Youall Goodweed, who is “into” natural foods. While I don’t always agree with him, his table talk usually is at least as nourishing as a fern and bulrush casserole from a recipe in “The Grazing Gourmet.”
On this occasion Goodweed was saying that what this country needs now is another oil embargo.
“Those were the good old days,” he sighed.
[…]
“Are you suggesting the Arabs resumed exports when they did because we were beginning to realize how fortunate we were to be without their oil?”
“No doubt about it,” said Goodweed. “Those Arab oil producers didn’t just fall off the turnip truck, you know. They’re smart enough to see the embargo was the start of something good.”

6-: From the column Personal slants, by Doug Kneibert, published in The Sedalia Democrat (Sedalia, Missouri) of Friday 14^th November 1975:

Nothing quite reveals the yawning expanse of the generation gap than your inability to distinguish between those words or phrases that are In, and those that are Out.
Take the other day. I had just asked my son whether he had remembered to do his homework, as he prepared to drive off into the night.
“Whatdaya think, I just fell off a turnip truck?” he asked.
Ascertaining this to mean that I had impugned his intelligence, I replied yes. And at this stage I would much rather have him in the bed of a turnip truck than driving one.
[…]
Lest my own children think the old man a total square (clod?) I decided the other night to show them that I could still dig the lingo. When my son’s friend drove up to show off his new car, I hit him with:
“Right on, man! This is too much, a real cool set of wheels. How much bread did you have to lay out for it?”
“Who’s this turkey?” he asked.
“I don’t know,” my son said, “but he sounds like he just fell off a turnip truck.”

7-: From a letter by Col. Herman Cofer, Commissioner, Georgia Department of Public Safety, published in The Atlanta Journal and The Atlanta Constitution (Atlanta, Georgia) of Thursday 27^th November 1975:

Atlanta—Well, it seems recent stories of our intent to seek legislative approval for more plain colored patrol cars to use in enforcement has brought out the die-hard speeders who scream “entrapment and hide and seek” and object to our fighting fire with fire.
[…]
As the old saying goes, “We didn’t just fall off the turnip truck.” We have tried, and are trying, every conceivable method known to be effective and fair with the motoring public.

8-: From a letter by one Frieda Gelph, of San Francisco, published in the San Francisco Chronicle (San Francisco, California) of Friday 5^th December 1975:

Bonanza!
Editor—From the December 2 Chron, the solution to the city’s fiscal problems:
“Two dozen copies of the original map of San Francisco went on sale at City Hall for $3 each.
“The Mayor’s office. . . said San Francisco and Clackamas county will share in the profits.”
Oh, wow! What a bonanza! A big $eventy-two bucks gross and the printing costs not over a hundred. Thanks Heavens for our alert mayor and his brain trust! Those guys didn’t just fall off the turnip truck!
New York please copy.