Yeah, I agree with kelly's advice here. Find a board or if you have a friend in the legal profession have them look at the lease...you have to remember, this is how the aprtments complexes make the big money. If I am understanding correctly though your lease requires a 1 month notice, which you say you have given, so the only way that you could be charged for 1 month would be if you have not given 1 months notice. The lease should specifically state 30 days, or in some cases 60 days. If it states "1 month" then I can imagine that if push came to shove you would win any dispute over the days in the various months chnge... The lease disputes are usually fairly easy to overcome, I messed up in the past and had to deal with a few of them. And if I have understood nothing of your post, and this makes no sense, forgive me please and pay no mind to my rambling.
Edit: Ok, I read your post again, so yeah, if you gave the notice on the 4th that you would be out on the first of Sept, yes it would be totally legal for her to charge you for the month of Sept. (not to mention it wouldn't be very nice, but this is how they make their money)
