I found another way to produce similar symptoms. I left it set for United States, but customized the date settings.
The default settings look like this.
The difference is that the short date format has been changed from mm/dd/yy to mm/dd/yyyy. With that setup, To enter the month numerically I need to enter it as dd/mm/yy. It displays in the MM/DD/YYYY format, when the output pattern is left empty.
This is similar to another problem reported in December.