They don't stipulate an FAA pilot certificate because they never considered people with non FAA credentials applying.
Don't be one of these people who get upset because you find out when you start training that you are not eligible for the CPP program or a flow or whatever else they said to you at interview. They don't tailor the recruiting pitch to non American.
Also, you can't put foreign ratings on an FAA pilot certificate. The FAA only recognise types done by FAA examiners using FAA approved facilities. Many have tried, all failed.