1) Except for sprinting, all cycling performance including short duration events like a 4 km pursuit are dictated by aerobic capacity.
I strongly disagree there. Long distance rides are not dictated by aerobic capacity but by muscle fatigue. In the last 2 years I can only think of one race in which I was short of breath before the sprint.
Different riders will hit different barriers and less trained riders usually hit the aerobic barrier first.
Ric's off the mark about cyclists not needing strength (hills, headwinds, breakaways and surges are a few times they do), but the difficult part is converting gym strength to bike strength.
I spend alot of time riding and racing into block headwinds and I'm always in need of more leg strength.
As John said in another thread, there is a difference between Lactate threshold and the anaerobic threshold. Often we sit above the LT and below our AT, and additional strength would mean we could go faster at that level.
First, your application of terminology is incorrect. When discussing exercise physiology, the term aerobic refers to those mechanisms whereby energy is produced aerobically (the oxidation of either fat or carbohydrate). While at first counterintuitive, aerobic energy production has very little to do with breathing, at least in the sense of breathing being a performance limiting factor.
The exact mechanism of fatigue is not known, but I can assure you it has very little to do with strength. Let me give you a real example. In another thread, Indurain's hour power is discussed. To date, this is thought to be the highest power ever sustained by an individual for an hour: 509 watts power, 284 kg m/sec^2 force. My personal best hour to date: 319 watts, 260 KG m/sec^2 force. Note that my force (strength) is only 10% lower than Indurain's! The difference? Cadence. 101 RPM vs 69 RPM (my best hour was on a hillclimb race, for which in retrospect I was under-geared).
From this example, you see power and strength are two different things and as Ric Stern likes to say and this example underscores, strength has very little to do with cycling performance.
At the end of a long ride, fatigue occurs for one or more of a variety of reasons: lack of substrate (glycogen), accumulation of metabolic waste products, dehydration, core body temperature rise and neuromuscular adaptation. In fact, neuromuscular adaptation is now considered more significant than perviously thought.
Aerobic conditioning, therefore, refers to the ability to minimize all of the above. Peripheral adaptations (increased mitochondrial density and capillarization) a result of long hours in the saddle allow for increase oxygen perfusion, increased efficiency, increased metabolic waste product transport and removal, better regulation of core body temperature and conditioning of the neuromuscular sytems to allow the muscles to use there newfound power. None of this come from weight training.