Ahhh, well... Here's where things are kinda weird. =) Some vehicles use the O2 sensors very heavily, but this motorcycle wouldn't be one of them. Most vehicles operate in two modes:
Closed Loop - This is where the vehicle operates by consulting the O2 sensors by using the O2 sensors to close the circuit of consultation. The O2 sensor's measurement is consulted, and the fueling is adjusted accordingly in an attempt to meet the particular O2 level prescribed in the O2 map, generally somewhere between 12:1 to 14.7:1. Since the sampling rate is very fast, the adjustments can happen rather quickly, but generally not fast enough to accommodate quick throttle transition or high RPM operations. That is where the next mode of operation kicks in...
Open Loop - Open loop does NOT consult the O2 sensors to make adjustments. Rather, it takes (in simplified terms) a) Throttle Position, b) Manifold Pressure (MAP), and c) RPM. With this 3-dimensional matrix, it adjusts the level of fueling, metering the amount of fuel by keeping the injectors open for longer or shorter amounts of time to allow more or less fuel to enter the system. This way, reaction time of the O2 sensor is a non-issue. This situation (open loop) happens when there is a rapid transition of throttle, or when the throttle position reads above 70% (roughly,) or when the RPMs exceed 3800. So, needless to say, a lot of the time, you're operating in this state.
So, when disabling the O2 sensors, you make the ECU aware of the fact that you ONLY want it to consult the TPS, RPM and MAP sensor rather than looping in the O2. The variance in the maps mean that there's a chance you'd drop from a state where the ECU was sitting at a rich 12.7:1 then tries to transition to a near-stoichiometric 14:1. This sudden switch of behavior is what causes the 'snatch' a lot of of people feel on both decel and decel-to-accel transition. This is very much exacerbated when you have a freer-flowing exhaust or intake due to the fact that the environment that the O2 sensors measure, the exhaust stream, can shift to an extremely lean condition very quickly compared to the turbulent, restrictive environment of the stock plumbing.
The system's 'adaptation' allows the adjustment of various levels of this map to a value of UP TO +/-10% of it's prescribed fueling at certain RPM, which makes it better suit the unique operating environment of your bike. But, this may not be enough adjustment in some cases, and it makes your map more unpredictable, since your adjustments will be adjusted around for the lower RPM/lower throttle position regardless of any changes you may make. This unpredictability is what a lot of tuners dislike, since every time you make a change, the bike will try and adjust around it to keep the results the same or similar to it's target O2 range.
Now, onto your question about air injection. Air injection does exactly what it sounds like; It takes air from the intake tract, opens a large metallic valve that allows that air to be drawn into an air passage that is connect to the exhaust side housing. This air that gets drawn (or injected if you will) into the exhaust acts like a reverse EGR system on a car. The air leans out the mixture, causing it to burn or ignite in the exhaust system. This means much lower levels of unburned fuel in the air, but instead of that, you get higher volumes of CO2 and NOX emissions. It's a bit strange and counter intuitive, but when you realize that advanced ignition causes more 'complete' burn at the cost of increasing NOX emissions, it makes sense. So, in light of wanting lower airborne particulates, we mildly adjust the level of air in the exhaust. The ignition happens, typically, at the hot part of the exhaust and after the point where turbulence doesn't prevent ignition. It's usually downstream from the O2 sensors a lot, so this change isn't measured or accommodated for by the map in any measurable way. The AI just 'functions', it doesn't consult the sensors in any meaningful way to adjust it's own behavior. It's a valve that is either open (decel, mid to low rpm) or closed (all other times.)
The air injection can, therefor, cause excess ignition in the exhaust itself, and cause reversion when this ignition happens, where the exhaust flow suddenly reduces it's laminar flow by the rather sudden introduction of a pulse wave that expands in both directions as a side effect of the ignition downstream in the exhaust.
Phew. So, what do you lose by shifting to O2-less operation, to step back? The adjustment is still cogent of the ATS (Air Temp Sensor, in the intake tract) and it knows about changes in elevation via the MAP (Manifold Absolute Pressure) changes that take place when your air density is lower, due to the fact that the air pressure would drop at higher elevation. You do lose a degree of the ability to run leaner mixtures on deceleration and low throttle input states in a safe manner, but this can be tuned into the map directly if it's the behavior you prefer.
I hope this makes it a little easier to understand the O2 sensor thing! Sorry for how wordy I was. =)