Grace period after expiration of H-1B?

Hello,

My H-1B visa (as well as my status) expires on September 7, 2006. I plan to leave the country and wonder if I have any "grace period" to do so. I asked this question to the BCIS officer at the border last time I entered the country and she said "10 days after the expiration date of I-94". However, from what I read on the Internet forums, half of the people say 10 days, the other half believes there is no grace period and I have to leave immidiately.

I wonder if anybody knows the law that clearly states whether it's 10 days or immidiately? Should I decide to remain, say, a week after the expiration of my I-94 would there be any problems in the future or the BCIS does not really care about such little overstays?

Thanks you in advance.

Gregory