Well, it really depends upon how tenuous your "proof" is, as well. I mean, if it's something as straight forward as a parent being Italian, then it's usually quite short. However, if there's something as silly as a spelling mistake SOMEWHERE they'll make you jump through all sorts of hoops. You'd think they don't even have fax machines or e-mail with how convoluted their communications can be.
With regard to Piazon, his agent or whoever said something along the lines of having "roots" in Veneto. That could be something really distant, so until they really do some proper digging, it could go on for a while.
They make exceptions based upon who you know, really. Typically footballers are high-profile and have money, so things get greased a little.