You really have a very strong background. If you really want to get into top stat phd programs, only applying for 2 or 3 schools is not a good idea nowadays. I think stat phd programs, like Berkeley, may have more requirement on math background. This may not be universally true, but personally I think it would be safer to take courses like real analysis and measure theory during undergrad. How many stat courses you have taken, on the other hand, actually does not add much points to get the admission into stat phd programs. Just as you said, you have taken no psych class and still managed to get in the psych programs. Rigorous stat phd training usually requires a lot of math work..... Anyway, maybe if you have tried Stanford, you probably have a good chance. I know they have sent out a lot more admissions to foreign students this year than last few years. Good luck!
