It's merely a suggestion of a route to explore from someone who has gone through the process. I have an American passport. It states my foreign place of birth. I have a birth certificate from the foreign country I was born which states both mother and father and their respective nationalities. I've lived my life in the US and as a child traveled many times without any issue on an American passport with only my mother to from South America (an without a letter of permission from the sperm donor). Of course this was pre 9/11.
On a side note, I have travelled over a dozen times with my children thoughout South America and Europe without my spouse and I have never been asked to produce a letter of permission front their father. I have always had one ready in case that has been notarized and translated into the current language. BUT, I have yet to be questioned as to my travels with my children and had any agents inquire about their father. I'm aware what is written about traveling alone with children but in my experience it isn't how it's been applied. Then again, there maybe someone else out there that has had a completely different experience. This is simply my own experience.
On a side note, I have travelled over a dozen times with my children thoughout South America and Europe without my spouse and I have never been asked to produce a letter of permission front their father. I have always had one ready in case that has been notarized and translated into the current language. BUT, I have yet to be questioned as to my travels with my children and had any agents inquire about their father. I'm aware what is written about traveling alone with children but in my experience it isn't how it's been applied. Then again, there maybe someone else out there that has had a completely different experience. This is simply my own experience.