You are correct in your thoughts. The trouble in these discussions is getting all those discussing to a point they are discussing the same thing. That is why I wanted to point out my stance or view is that of a traditional old school type lifter, but to be even more specific that it is more in line with power lifting movements - squat, deadlift and bench. I trained and consulted in a gym that had world class Olympic Lifters that had set world records. It had world class powerlifters like the late Dave Pasanella and Curtis Leslie that both were squatting near or at 1000 lbs. It had national and pro bodybuilders and the gym was owned by one the of the world's most popular Olympic Lifting coaches for USA women. Not to mention all of those like myself that were top notch local and national level athletes. If you gather all of those people together to have a big round table discussion on strength and how to gain strength there would be some similarities and some agreements, but there would be a lot of disagreement as well. Part of the disagreement will become the definition of strength and much of the disagreement will become the definition of it. Yet all of those people have had great success despite different training principles and different training philosophies. Yes, there is science in that mix.
From my perspective it really comes back to specificity and that part I cannot get past. For me it always comes back to specificity.
You adapt at what you train. Like you said about P90X is the same claim to fame for the CrossFit franchise. CrossFit makeup is to always train without structure so that each day
you don't know what you are going to do until you get there kind of theme. But I say that is a load of **** because in the disorganization there is still specificity even if they think there is not. They do chin ups. They do deadlifts. They do clean and jerk. There are some things they do train regularly even if it is not a regular schedule. When they get to competition they can do chin ups because they have trained chin ups. The difference comes when they throw in something completely random like a version of a triathlon. They looked horrible in doing that triathlon. Sure they have some good cardio conditioning and they did make it through the event, but when compared to people that actually train specifically for triathlons it was pretty pathetic. The CF's then looked pretty amazing when they get to events that they train like deadlifts, clean & jerk and pushing a weighted sled because many of them train that. Just like you will become good at P90X if you follow the video in a progressive manner and those movements. Let's say that I train in power lifting and I have progressed well, but then you and I have some sort of P90X competition against you after you have done many months of P90X? You would probably do better than me because the strength that I gained in specific movements like bench, squats and deadlifts are not going to be the same as what you have gained training randomly through the P90X. You will be able to hold a plank far longer than I could because though I have a strong core from doing deadlifts and squats it is not the same as actually adapting to doing planks.
So it is a very difficult topic to discuss. If Tudor Bompa and Dr. Mel Siff had disagreements on the terms, philosophies and science than it really is a difficult topic. Current day world class strength coaches like Dave Tate and Charles Staley having a disagreement on Box Squats.
http://staff.washington.edu/griffin/box_squats.txt
As far as glycogen use in anaerobic training that too goes to the type of training. So I am talking about a few sets of heavy squats to improve strength, whereas, you are talking about P90X that is how many minutes of virtual continual movement? I forget how long the DVD session lasts, but for improving strength in squats during my offseason was very heavy weight for low reps. Each set was no more than 6 reps lasting less than 10 seconds and could have up to 10 minutes of rest between sets. I don't think I used much glycogen during the strength training periodization, but then again that is under my definition of strength training. During my pre season preparing bodybuilding competitions I would often train with heavy weight while being intentionally carb depleted. I did that for many years and could still lift fairly heavy while being on a very low carb diet. For instance I had no trouble doing 405 lbs x 8 reps while being carb depleted, but I doubt I could have made it through a P90X workout while being on that same carb depleted diet.
My point goes back to comparing apples to apples and when it comes athletes in different activities the definition of aerobic and anaerobic, power and strength seem to take on different meanings during the discussion.
What is important is find what works for you to meet your goals and if you want specificity even if you are talking long distance cycling and kickboxing at the same time.
In the late 90's at near the peak of my "strongest" days in the gym I was also sparring with a Muay Thai kickboxer. As far as I know, and he rented a room from me so I had a pretty good idea of his training methods, he never did any sort of resistance exercise. Not a single push up or any other type of exercise. All he did was fight and spar. The power in his kick was incredible. The first time I held a bag for him to practice kicks he almost broke one of my ribs because I did not take his kicking power seriously. It literally lifted me off the ground and pushed me back about 4 feet. Yet absolutely no training outside of fighting, practicing technique and sparring many hours. Years later he was a sparring partner to several big name MMA fighters in the UFC.
Specificity for Bob in what he did for kickboxing seemed to work quite well.
I have a female coworker that looks incredibly anemic and thin. I doubt she could squat her own body weight and probably could not do but a few push ups. She really looks fragile and actually looks like a girl that should be walking the super model runway. She is very attactive, but very feminine in appearance. Yet she has won her age category in almost every triathlon she has entered this year by doing specifics of running, biking and swimming. She has trained, adapted and succeeded in her event with specific training and strength does not seem to be a factor or an interest to her.
I know this doesn't answer questions and it probably creates more questions. There are many roads and cross roads to the discussion.
Best wishes.