It all bows down to what you mean by "rich". Depending on how you define the wealth of a nation, you can get very different results.
Here is a link that describes seven ways to compare the dollar of 1774 to the current one. It has other examples of such comparisons (in UK, Spain, ...). The most ancient one is with the 1270 pound. For each comparison, it uses a wide range of indicators separated in three categories (comm). In short, for each indicator, you have to pick the commodities, incomes or projects the Roman empire (or another country) could buy/provide/finance. Then, once you picked these, you combine them and compare it to the same indicators for modern US.
Regarding commodities, it summed up to asking questions such as "how much pounds of flour could the roman empire have purchased"? For most commodities, the contemporary US would be advantaged, since the means of production are much more efficient.
Regarding incomes, it can be summed up to asking questions such as "how many people could the Roman Empire employ as state worker (or some equivalent)"? The low cost of hiring a slave or convincing someone to do a 20-year long military service in ancient times would definitely give an advantage to the roman empire. However, the US population being larger, it could still catch up. Note that for an honest comparison, slavery should probably be banned.
You also have relative questions, like "what is the percentage of this country's GDP compared to the world's GDP"?
Once you get your answer, it only has meaning with a full description of the indicator.
In order to remove ambiguity and still be right, Mr Sanders could have said something like "the US is the country able to make the biggest pile of hot dogs in the history of the world" (indicator: ability of a country to pile pile up hot dogs). However, it is not really appealing in a political meeting.