Some people have suggested that he had something quite different to release but didn’t want to interfere with the breaking coverage of the Benghazi emails...so he invented something that frankly wouldn’t cost him anything since he probably already gives more than $5 mil a year to charity (and, on top of that, he knows Obama won’t take him up on it anyway).
As for Obama: he doesn't have to release anything. Releasing it would be a sign of weakness, and would be seen to be an American pResident jumping to the tune of a private citizen that appears to be blackmailing him. Also consider this. a) Obama knows that those against him would never believe any records he released were genuine. b) Obama also knows that those who support him would be on his side even if it was shown he came from the planet Neptune. Thus, for him releasing the documentation adds absolutely no value. The only focal point would be the impact (or lack of) on undecided voters. So far, the undecideds were waiting for some bombshell, which never came. The statement by Trump does bring the fact that this president is hiding a lot of private information, but in and of itself will not sway an undecided one way or another. Similar to how releasing Obama's thought-about-divorce-years-ago information would simply have had no impact on undecideds (especially considering most of them have probably, at one point or another, thought of divorce). Unlike FReepers or DUmmies, undecideds and independents do not sway to the usual triggers we at FR or the silly ones at DU do. Think of it another way - they are actually undecided in one of the most important elections in US history! That says a lot.
Which is why I am amazed that some here think what Trump did was some amazingly Machiavellian master-stratagem, when the truth is that its impact is only on two groups. The FReepers (and other active Conservatives), a constituency that already considers Obama an usurper who is not American; and the DUmmies (and other active Liberals), a constituency that considers Obama the second coming of JFK. Neither of those groups is going to change their perceptions and perspectives. As for the Undecideds - it will take more to push them one way or another.
Anyways, I agree with you. There was probably some other story - an actual bombshell - which, for whatever reason, was put on hold at the last minute. Trump didn't make all the noise he made over the weekend just to make a YouTube video challenging Obama.