I think this is correct. According to the second draft of the screenplay, which I think can justifiably be appealed to here, Turnbull fed Tom a string of lies about Geary being squeamish about being bribed in a direct fashion (rather than through a "charitable donation to a cause Geary controls," as Tom puts it in the 2nd draft), so of course he and Michael were quite surprised when Geary came out swinging with his hefty demands. I'm actually inclined to think that Michael might have been under the impression that Geary's bribe money was to be a cut from the "magnificent contribution" to the university. The rest was for the purpose of polishing Michael's public image. (Notice that Geary, when speaking to the guests, doesn't say how much the check is for -- the amount of the donation to Sicily in GFIII is made explicit, and in general large donations to universities are announced, in press releases, etc., with the dollar amount specified.)