Reagan was elected with 51% of the popular vote to Carter’s 41% and carried 44 states to Carter’s 6(+DC), tallying 489 electoral votes to Carter’s 49. This was not a close election.
Hamilton Jordan, his chief of staff, wrote a book about Carter's last year in office. A lot of people thought Reagan was a clown. He was not as popular as his worshippers in the GOP like to think. Reagan was usually ahead of Carter in polls before the election, but usually by a few points, not the same margin as the final count.
The hostage crisis started on Nov 4, 1979; the one year anniversary of the hostages being taken was right on election day. A lot of media was running stories on the hostages in the week leading up to the election, particularly over the weekend. Jordan says there was a shift that took them all by surprise in its speed and magnitude. When you spend months only a point or two behind, it is easy to think you might win.
> None of that establishes whether Mr. Reagan knew about the trip, nor could Mr. Barnes say that Mr. Casey directed Mr. Connally to take the journey. Likewise, he does not know if the message transmitted to multiple Middle Eastern leaders got to the Iranians, much less whether it influenced their decision making.
"Historical fact" is a very strong way to say "one man's story recounted 40 years later and backed by modest circumstantial evidence", and even to the extent the story is true as told in that article, Reagan's backers didn't "conspire" with anyone—as recounted, they never spoke with the Iranians, they told other Arab leaders to let the Iranians know.
If true, this is still worth recounting, but you're not helping anything by overstating the degree to which we know this to be fact nor by overstating the crime.