The ATP cycle sounds right.. My physiology is rusty..

ATP is broken down to form ADP, and CP is another reservoir in which ADP can resynthesize back into ATP. There's more CP in the body than ATP, and ATP can't just be replenished by blood or tissues when depleted, it must be resynthesized in the mitochondria - which requires a food source (limitations of ATP)
In order for fats to be used as energy, a certain amount of carbohydrates must be broken down in order to ensure that the Krebs cycle (which is how fats catabolize) can continue. My brain thinks that this is why we have the short high energy bursts (carbs) followed by the moderate recovery (fats) to promote the highest amount of lipid catabolism possible.. This instead of a purely steady state which uses both carbs and fats but at a possibly lower level of fatty acid manipulation. So yeah, I think you're on target!
Or maybe I'm crazy.
Oh and the theory of lactate prohibiting FFA metabolism could be right... I know that it inactivates certain enzymes. And lactic acid is stored with pyruvate until a later time when oxygen is available to break it down, which directly affects FFA breakdown because they require oxygen. Hence, that 5 minute break which allows the respiratory cycle to regulate and oxygen to become available again.
ATP (adenosine triphosphate - that means three phosphates, folks) fuels muscle cells by breaking off a phosphate, forming ADP (adenosine diphosphate - two phoshpates are left) as the ATP is used to provide energy. Simple math will tell you ADP increases as ATP is broken down for energy.
This increase in relative ADP concentration activates AMPk, an enzyme that stimulates both fatty acid oxidation and glucose uptake in skeletal muscle.
Acute activity induces a sudden energy-need at the cellular level. The energy produced from phosphate breaking off ATP is useful for extremely short bursts - say under 10 seconds.
When ATP is high enough, and excess energy is available, it is stored (through the phosphate) as CP. The phosphate in CP is not immediately available to the cell as energy, but it is a compact energy storage unit for phosphate which is required to regenerate (from ADP and phosphate) ATP - which is the only available energy source to the cell.
My thinking is that ATP is the energy handler. CP is the non-user-friendly storage space for P. ATP hands off P for energy, then picks up P from CP so it has it available for the next energy request. At least, that's how it makes sense in my little brain.
Anything lasting longer than this requires glucose. The anerobic combustion of glucose results in lactate.
For the 8-seconds sprinting, 12 seconds of recovery sprint protocol, the acute energy need of the cell increase the ratio of ADP to ATP, which activates AMPk. In doing so, fatty acid oxidation is increased. Because the sprints are so short (ie under the 10-second threshold), glycogen is spared. This is a "pure" ATP protocol.
Now, the sprinting stimulates catecholamine release, promoting lipolysis. ADP:ATP increases, AMPk is activated, promoting fatty acid oxidation.
Marriage made in heaven, right?
Sooo... you do the sprint, you stimulate catecholamine. This promotes lipolysis of peripheral stores. If you go beyond 10 seconds, you go into the glycolytic pathway, producing lactate as a byproduct of the incomplete (ie anaerobic) combustion of glucose. But we don't go this far - and it appears that it's the lactate that prevents FFAs from catecholamine-induced lipolysis from hitting the blood-stream. This was the part Romjin et al discovered in their ground-breaking research a few years back, and which is why Lyle has people sit on their asses and wait five minutes after doing stubborn fat loss protocol before doing the SS cardio which follows.
I may have bits of this wrong. I'm still working it out.
Anyone? Anyone? Bueller?