Between the theory that the Romans came to America and the theory that coin collectors scatted coins around the country, couldn't there be a much simpler and logical explanation for older coins being found.
When you were a kid, didn't you collect coins? I don't mean real coin collections, but just collecting anything that was different, and never even knowing their value. I have always been collecting odd coins, but when it came time to buy some chips or sweets, or even later, put a gallone of gas in the car, I spent everything. Old coins are found in tot lots too, but I doubt that someones Indian head penny fell out of their pocket a hundred years ago. Kids get a hold of coins at home, or friends house, and eventually they are lost. I'm sure through out the history of the US, there have been people with odd coins in their pockets or purse, and eventually these coins ended up in collections, or more likely, lost or even thrown away. After WW1 & 2, there were many things brought back from Europe, including old coins. Some people may have realized their value, but to others, they were just odd, and of no value.
I wonder how many fortuns I have thrown away, not knowing the value of old coins, or what sterling even meant! That's why flea markets are such fun, there are still a lot of people that don't know the value of an item, and others that do.
I just dint see the mystery of finding a coin that doesn't belong there.