Lets talk about coins turning up in odd places. It is a common occurrence. The best survey on the subject was by Epstein who looked at 40 accounts of Pre-Columbian coinage in North and South America. He noted a few early examples, but a remarkable increase in the post World War II era....corresponding to a time of dramatic increase in American visitors to places where Roman coins could be purchased cheaply. He felt that all such Pre-Columbian Greek and Roman coins were either lost by collectors, or in a few cases were examples of fraud.
Roman coins have turned up in pig pens. And in the ruins of a Louisiana bus station. And in a Los Angeles parking meter!
A couple of cases warrant specific discussion.
The earliest account of a Roman coin in the New World comes from Panama in 1533. Unfortunately this story of a gold coin of Augustus turning up has no further mention in history, and is to be found only in a rather fanciful work that recounts various miraculous events occurring around the birth of King Ferdinand.
Another South American find was said to be a hoard of several hundred coins ranging from Augustus to 350 AD, a range far too broad to be anything other that the lost collection of an early aficionado.
This report Panama find comes from the New York Times. (you will have to scroll down a ways to see it). As it again reports the extraordinary circumstance of a hoard it might be a re-telling of the earlier hoard from, apparently, Venezuela. One assumes that the Times, even today viewed as widely truthful unless discussing Republican politicians, might also have been snookered by an unscrupulous correspondent.
We can only smile about the apparent coin of Maximus that turned up in the Seip Mound in Ohio. On careful cleaning it proved instead to be a "portrayal of Father Time which appeared on an Elgin Watch Company token commemorating the Chicago Exposition of 1874".
The Bar Kokhba coin and these specimens from Kentucky and Ohio:
Archaeological Outliers here.
So most of the common Roman coins that are found in the Americas have mundane explanations. They were modern imports that were lost or much less often used as hoaxes. A similar situation exists in Britain with Alexandrian coinage. These local issues are never excavated at Roman sites, but turn up in parks and gardens with some regularity, reflecting nothing more profound than the frequency of travel to Egypt.
But a very few cases raise doubts. After all, a rather minimal Norse presence did leave behind one accepted coin in an Indian mound in Maine. Genuine Pre Columbian! So just maybe...
In 1964 a Native American site at Round Rock Texas was excavated with some speed due to an impending freeway project. Three feet down in a mound a follis of Constantine the Great was unearthed. Minted in London in 314 it was certainly out of place surrounded by stone implements.
You could envision a storm tossed Roman ship washing up in the Gulf of Mexico. It is more or less the same course Columbus ended up taking, albeit with better ships.
Unfortunately the excavation of the site seems to have been hurried, done by a mixture of amateur treasure hunters and a quick survey by professionals. The observations of the latter were that the stone artifacts were above the reported find site of the Round Rock follis, and were substantially older.
This suggests disturbed stratigraphy. Advocates of the authenticity of the find are vocal, and point to the hard rocky nature of the site making disturbance by vegetation unlikely.
The site was effectively destroyed by the construction of I-35, so as you drive past at 65 miles an hour you do not have much time to ponder the mystery.