Of course it is often hoped that an accismus will lead to another offer and perhaps even an emphatic insistence that you accept, until you are able to convince yourself that you weren't being greedy, that you didn't have to restrain yourself from yelling "YES YES I WANT IT!" or, if the thing offered was something present and tangible, snatching it out of their grasp. A really successful accismus results in a sort of role reversal, with the offerer's expressed desire for you to just take the last cupcake already becoming as ardent as your unvoiced desire to have it, and your urge to say yes transforming from something borne of greed to something motivated more by altruism -- a desire to kindly indulge their need to give it to you and not embarrass them by refusing yet again.
People are weird, man. Really, really weird. If you've ever doubted it, the existence of this word ought to make a believer out of you.
Of course employing an accismus can be a perfectly respectable strategy if you're dealing with someone, like a spiteful sibling, who would react to you expressing your desire for something by claiming it themselves and then flaunting their ownership of it, possibly by destroying it in front of you. One can also be successful even if the offerer doesn't actually browbeat you into taking what you claim not to want. Say "Ohh, no. What would I even DO with a Rolls-Royce, Grandmother?" enough times and leave the will reading with the keys in your pocket. Spend too many deathbed visits flipping through car magazines and you'll be lucky to get a stack of old National Geographics and an incontinent dog that, by all rights, should have preceded your wealthy relation to the grave.
Accismus comes from the Greek akkismos meaning "coyness," "affectation" or "prudery."