Though I live in Texas, a state that leaves it up to the districts, I have seen some of the districts take this approach. They will not allow early entrance to Kindergarten and no amount of tests will change their mind. And for the 1st grade requirement: our state is the same way. Only if the child comes from outside the state. BUT I do know that this does not mean that the child will not be able to advance to 1st grade when they enter Kindergarten. One friend of mine plans to send her DD to public school and her DD missed the cut off date by 2 days. She is a smart, mature little girl and was clearly ready for Kindergarten this year but the district will not even consider allowing her. They will, however, test her during the first 2 weeks of school (next year) to determine if she needs to skip to 1st grade.
So even though your state has the same 1st grade rules that ours does they might also allow for acceleration, bypassing Kindergarten.
This is how it is in our district. I live in GA. There was NO way around the K rule for DS6.5 (December birthday), but as soon as he was in K he was tested and moved to 1st.