This story was updated with Ford's response.

Donald Trump is taking credit for a decision by Ford Motors to shift work from a plant in Mexico to a plant in the U.S., tweeting on Sunday:

Word is that Ford Motor, because of my constant badgering at packed events, is going to cancel their deal to go to Mexico and stay in U.S. — Donald J. Trump (@realDonaldTrump) October 25, 2015

What is he talking about and how much credit can he claim?

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Over the weekend a few blogs, crediting another site called Prntly, celebrated Trump's impact on Ford.

"Under pressure, Ford is moving back their Mexican plant (worth 2 billion) back to the states... Youngstown, Ohio to be exact. There will be 1,000 new jobs for factory workers there. I'm sure I'm not alone with an urge to weep in relief over that one development. Ford must believe that Trump will be the next president," the post on Prntly read.

It appears Trump was responding to these news items, sourced to Prntly.

But the news Prntly is so moved by is a couple of months old. It refers to Ford's August announcement that it had begun production of 2016 medium-duty trucks in Ohio. It is true, as the site mentioned, that 1,000 jobs would be shifted to Ohio, and according to Ford's press release, it was also true that the trucks had been "previously assembled in Mexico." But this is no $2 billion deal -- it's $168 million. And the jobs are in Avon Lake, not Youngstown.

As for the pressure from Trump, he mentioned in his Tweet that it must have been his "constant badgering" that changed the automaker's mind. He is referring here to threats he made on the day he announced his presidential candidacy in June. The billionaire said he'd slap a huge tariff on every Ford produced in Mexico and told the U.S. automaker so in his speech.

"Let me give you the bad news: every car, every truck and every part manufactured in this plant that comes across the border, we're going to charge you a 35 percent tax -- OK?" Trump said. It was a line he repeated several more times on the campaign trail.

But John Kasich heard about Trump's tweets and is probably justifiably irritated because, as it turns out, the credit for those Avon Lake Ford jobs appears to belong to him. In 2011, Cleveland.com reported, the Ohio governor negotiated with Ford for the jobs and secured $15 million in tax breaks for the automaker over 15 years, to entice Ford into keeping the jobs in Avon Lake.

Kasich took a swipe at the billionaire over his tweets, which Kasich called "empty, false rhetoric" in a statement Sunday. "We brought Ford production jobs back from Mexico to Ohio years ago," he went on to say.

Ford, on Monday morning appeared to confirm Kasich's version of events. "Ford has not spoken with Mr. Trump, nor have we made any changes to our plans. We decided to move the F-650 and F-750 medium-duty trucks to Ohio Assembly in 2011, long before any candidates announced their intention to run for U.S. president," the statement read.

Trump's original threats were actually in response to a different deal -- Ford's April announcement that it would invest $2.5 billion in new engine and transmission plants in Chihuahua and Guanajuato, creating 3,800 jobs.

The fear for U.S. auto workers is that those jobs are coming straight from Wayne, Michigan, where Ford workers were informed in July that the cars they produce -- the small, fuel-efficient C-Max and Focus -- would no longer be produced in the U.S. The Wayne plant employs 4,000 workers.

In any case, it seems that the answer to Trump's question below -- should really be "No."

Do you think I will get credit for keeping Ford in U.S. Who cares, my supporters know the truth. Think what can be done as president! — Donald J. Trump (@realDonaldTrump) October 25, 2015

CBS News' Alan He and Katiana Krawchenko contributed to this report.