"require additional oxygen to "catalyze" the fuel, without the air pump they may 'clean' the exhaust, but they act as a filter rather then a combustion unit they were intended to be."
Close - but not quite right. The cats accelerate (or catalyze) further oxidation of harmful emissions components (HC, CO and NOx). That oxidation chemical reaction combines free oxygen with those harmful compounds to transform them into H2O, CO2 and N2 - non-controlled emissions. They will help the oxidation occur to the extent there is free oxygen in the exhaust stream to support the chemical reactions. The air pump is there to be CERTAIN there's enough free oxygen to support further oxidation. The cats are there to accelerate the process. The cats have no "filtering" capability. They are simply precious metal compounds (the 'catalyst') laid down on a ceramic substrate. As the exhaust passes over it, it catalyzes further chemical reactions. If not enough free oxygen is present to support the further reactions, the cat does nothing at all - except provide a bit of a flow restriction. The cats 'plugging up' that seems to be accelerated if the air pump isn't run isn't connected with the cats doing any 'filtering' type exhaust cleaning. Rather, deposits on the ceramic substrate seem to occur (much like mineral deposits in an old radiator) in part because with the lower level of oxidation, the temps in the cat don't get/stay warm enough to 'burn' those deposits off more effectively. Even the proper operating ones will 'plug' up over time.
89Mustang - not doubting that you've passed the tests over the years. But you can't generalize your situation to anyone elses. Each engine is unique in how it runs/is tuned/is modded. Each testing facility is unique - each testing tech does things their way - the testing equipment may be calibrated differently. And certainly in different parts of the country they're looking for different things. Lastly, the emissions equipment on the cars was designed to control emissions below a certain level for 50K-100K miles (it's changed over time) - by law. That's a HUGE range of changing operating conditions to control within. It wouldn't surprise me a bit that a vehicle could pass - under certain conditions - without an air pump, or without cats or even without egr. That DOESN'T mean it's prudent to conclude that because yours reacted a certain way that everyone else's will too.