Enforcing illegal torrents failed. I think a cryptocurrency ban would be similar. Also, the US made it illegal to hold gold between 1933 and 1974 but almost nobody turned in gold to the feds. https://en.m.wikipedia.org/wiki/Executive_Order_6102
Both are essentially electronic systems of information on a computing system, a format and a protocol of communication through the internet. In terms of technical difficulty to enforce them it would be very similar.
I'm pretty sure that "They" was meant to refer to the Government. The Government could most certainly pass laws (or enforce existing laws) that put people in jail for accepting stolen or "dirty" coins. (Just like the Government could pass a law or re-interpret existing laws to make making owning bitcoins illegal.)