Guess it depends on your geographical location.
This is just as offensive as saying that Caucasian men should be with Caucasian women.
But I agree with you.
Do Japanese girls like American men? Most of the time, you will be aware of low door frames and the like and therefore take care.
Funny accidents are bound to happen.
Once you get to know her you can determine if she is open minded.
An online survey conducted by Japanese site My Navi Woman asked 215 Japanese women between the ages of 22 and 34 what they like about shorter men.
Because I was dressed well and look like I have my life together.