I would go with the date it was sent, since there's pretty much no way for them to know exactly when you received the letter.
Plus, I personally don't believe the admissions office to be so strict on that, like I don't really think they would revoke your acceptance, unless you mail back your letters like way way way late.
I spoke to someone on the phone when I called to ask about my payment getting through, and I asked him when the due date was for the forms exactly, because I had sent them in pretty close to that two week deadline of the letter's date. I think he told me something along the lines of "Acceptances should go out by April 15th so I would say your deadline is the 15th"
Also, those who have paid for NASS already, does the $350 still show up on the payment site after you enter your information?