Any decent machinist with a fairly simple set of tools can knock up high quality devices if they have a set of plans. If you've access to the latest types of CNC machinery it's even easier. Ever watch those programmes on Discovery about car and bike builders ? Watch the kit they use, it's not hugely expensive or particularly new but can turn out precision parts quickly. Then all you need is detonators and an explosive fill and frankly Iraq is awash with that sort of thing as Saddam dispersed ammo stocks pre invasion.
Plans can easily be smuggled across borders and the Iranians may well have sent a few copies over - but the Iraqi weapons industry was capable of producing their own, and feedback from operational use helps to refine designs as well.
As for mortar attacks, all you need is an Iraqi who remembers using them in the Iran-Iraq war. The Iraqis used firepower to negate the Iranian manpower advantage and got rather good at it. Besides, they've had enough time on the live fire range to weed out the biffs and hone their skills.
I'm afraid that this is just more senior officer naivety - a number of smugglers were stopped crossing the border last year carrying IEDs; I don't believe that the problem has gone away. If you can't find anything it usually means that you are looking in the wrong place; to be so flippant about the problem undermines the efforts of all and, particularly, the deaths of our soldiers. To take the word of the border guards is, quite frankly, extroardinary.
One of the main problems is that a large number of Iraqis fled to Iran when Saddam was on the throne. They have since returned funded and helped by Iran - these people are in government and in the militia where they play a significant role in the way the country runs.