They're both right, and, as you've spelt out the month, there can be no misunderstanding.
Misunderstandings DO arise when we see, for example, ' 11.06.05' from British people, and '06.11.05' from Americans. Unless one of the day or month years is higher than 12, there is no way to tell whether it means 11th of June, or 6th of November.
In Britain we list in order of size: day (smallest unit) first; month (middle-sized unit) second; year (largest unit) last. So today it's 08.12.17.
But Americans start in the middle (month), then list the date (smallest), then the year (largest).
So today for Americans is '12.08.17'.