I think that the waiting process is to make sure that you're healthy enough. If you can get through both rounds of waiting (heart palpitations, knotted stomachs, etc.), then you should be able to pass the medical exam.
I think that they work under the assumption that you're going to accept. In the last line of the acceptance email they say "If at any time in the coming months, you determine that you will not be able to accept the Fulbright award, please be sure to notify IIE immediately." Hope this helps.