Decoding the Past ran from 2005-2011, but remains in syndication. This episode dates from 2006. The producers seem mostly interested in the paranormal, but also have an obsession for "secret societies." I thought one of the most amusing aspects of "The Secret of the Dollar Bill" was the attempt to link the Illuminati with the Founding Fathers by inferring that there was correspondence between Adam Weishaupt, the founder of this group, and Benjamin Franklin. Weishaupt apparently wrote to Franklin but there was no record of Franklin ever responding.
Benjamin Franklin was a freemason, as were many of the leading American politicians of the time. The Illuminati adopted much of the imagery of the freemasons, including the eye of providence, which is featured on the one dollar bill, but this all seeing eye dates back to Medieval Christianity, but by the 18th century had come to be a symbol of the Enlightenment and didn't necessarily refer to God in a Christian sense, but rather as benevolent guidance. The Eye of Providence over an unfinished pyramid was designed in 1792, with thirteen steps and the date 1776 to represent the original states and the Declaration of Independence, suggesting the influence of the Enlightenment, not the Illuminati.
The dollar bill in question didn't first appear until 1935, not 1862 as suggested in the television show. Salmon P. Chase appeared on the first dollar bill. In fact, Chase was featured on all the currency at the time. One of the perks of being the Secretary of the Treasury. The back was rather prosaic. George first appeared in 1929, but it was a silver note and the back looked like this. The US Mint kind of went overboard with the idea of "13," on the 1935 dollar bill, which has fed conspiracy theories ever since, including those who see Satan in the dollar bill. I guess the stamping of "In God We Trust" in 1964 on the bill was supposed to eliminate this suggestion, but sadly this theory still persists.
I understand that these conspiracy theories are great fun, but when packaged as "history," these theories become incredibly misleading. Best to file it under fiction.