There's no special agency that doesn't answer to anybody. As president, Obama is also responsible for enforcing laws. He has every right as part of the vetting process to give law enforcement agencies veto ability (or not).
There are some special rules for the Office of Public Accountability, but they're for investigating officials already in power. Even then, I don't think you get around the Executive Branch running the FBI. The president, as chief law enforcement officer, can muck around in any ongoing investigation he deems he should.
Despite being part of the criminal division of the DoJ (and therefore under the Attorney General who is appointed by the President) the FBI's governing body is Congress.
However he does have some pretty broad vetting tools. I believe that is generally coordinated by the Secret Service, who has access to all levels of police report. It's therefore almost inconceivable that they didn't know about this.
The FBI was created by the Justice Department. It is entirely inside the Executive Branch. Its leader, like other cabinet officials, is appointed by the president and confirmed by Congres, although he serves a 10-year term. As Nixon clearly demonstrated, the heads of these agencies serve at the pleasure of the president (http://www.washingtonpost.com/wp-srv/national/longterm/water...) More recently, Clinton got rid of Sessions http://www.slate.com/id/2066861/
Like all Federal Agencies, the FBI has close relations with Congress, which approves its budget, tells it how to operate, and investigates any wrongdoing. But policy decisions -- how to execute the laws in place -- are made solely by the President.
But none of that looking told me anything I didn't already know.
No, I think it is pretty clear they are. He's already tried to appoint about 5 tax cheats, most of whom were shot down because of that (I think Gheitner had some tax problems but was still confirmed).
This has to be one of the most amusing cabinet appointment periods in history. I forget how many train wrecks it took, but eventually I started laughing out loud over the new ones.
"More to the point, the Obama administration could have the worst vetting team in the world and they'd still be smart enough to ask the FBI if they had any active investigations on the appointee. It's too rudimentary a step to skip."
I'm still sure the vetting team checked specifically into Mr. Kundra but I have to admit this makes them look a tad incompetent. They may not be the worst vetting team but the fact that the President seemingly didn't know this was coming does not reflect well on them or the Administration.
(In my original comment I assumed the vetting team knew this raid was comming but disregarded it because there were no direct ties to Kundra)