Do American users also confuse the day and the month in dates like 01/02/2013

Almost everywhere outside the United States, when short dates, e.g. 01/02/2013, are shown on computer screens, the user can’t be sure whether the first two digits represent the day or the month. Is it January second or February first?

This is a big problem for people outside the United States, as they encounter both formats regularly, and can’t know if the system has adapted to their locale, or has stuck with the American format. But I assume American users see mostly the American format (because many, if not most, information systems are built by or for Americans). What I’m curious about is whether American users also are confused in this scenario?

If you can point to some evidence or research, great. If not, I’ll settle for your knowledgeable experience.

Note: I’m not asking for the wonderful solution of naming the month, e.g. May 21, 2013. I’m asking about the cases where a short date format has to be used.