What? That was absolute BS. The mechanic was just telling you that because he couldn't figure it out so he wanted to give an answer.
The O2's and smog pump and EGR are totally different systems. All the o2's do is measure the amount of o2 in the exaust.
The EGR (exaust gas recirculation) takes exaust gasses and puts them back into the intake. This reduces combustion chamber temps reducing NOX emmisions. Now the system is controlled by the EGR solonoid, which if the EGR valve or solonoid was malfunctioning it could be opening the EGR at the wrong time. The EGR is supposed to only be open durring cruise and deaccerleration, if it is open durring load or idle it will cause a bad miss. Try disconnecting the EGR valve and see if that makes any difference.
The smog pump is just an air pump. It is an example of 1980's emmisions technology, it is supposed to feed air to the cats to make them more efficient. That is why there are two lines, one to the 2 lower cats and one to the back of the heads. The one to the back of the heads feeds air into the exaust ports themselves, for the 2 upper cats. There are vaccume controlled solonoids which tell it when to open and close.
For a low end miss, check plugs and wires first, as well as any vaccume leaks. I just never have heard of the air pump deleted causeing a miss.