Vetting is very much in the eye of the beholder. Losing campaigns almost by definition claim their opponents weren't submitted to it -- see Clinton '92, Bush '00, not to mention Obama '08. And even beyond what happened in a campaign, after a guy has been president for a few years 'vetting' him becomes less significant since the whole point of 'vetting' is to give us some indication of what he'll be like as president.
But beyond these sorts of logical arguments, it's difficult to see Brisbane's prod as anything but a dog whistle to the far right crowd who holds up for the idea that there are as yet uncovered sinister facts about Obama's identity which might show him to be quite something else from what he appears to be. Brisbane asks "Who is the real Barack Obama?" To which the only real answer can be, just what does that kind of rhetorical question mean?
Can anybody point to significant questions about President Obama's history or identity that remain to be probed? That is, beside the questions about birth certificates, 'radical associations', religion and so forth that animate the American hard right? Everything else in Brisbane's column might be generously interpreted as a call for tough campaign coverage of the president. But in this question makes that impossible.
David Corn noted last week that the Romney campaign has been working to mainstream that idea that President Obama is somehow not a 'real' American. But Brisbane doesn't seem to need persuading.