Sadly, this isn't true at all when applied. We actually train 200m athletes for the 400m much more frequently. The weights to sprints analogy isn't quite right.
Low rep, heavy weights: dominantly phosphagen pathway, with some glycolytic depending on how long you take.
Push ups: nearly entirely glycolytic.
200m sprint: mostly glycolytic. It's about a 60% glycolytic, 40% phosphagen split. The utilization of the phosphagen pathway is explosive and intense.
400m sprint: mostly glycolytic - so much that it nearly drains the glycolytic pathway. This is why we training 200m runners with 400m's frequently. Since their glycolytic pathway is being utilized frequently, the body may convert fast-glycolytic fibers to fast oxidative glycolytic fibers. These tend to jump into the game as quickly as fast-glycolytics, but have more oxidative capacity. More likely the adaptation is due to increased enzyme concentration to support the pathway. The glycolytic pathway is the majority of the 200m race so the carryover is astonishing - not in the start of the race, but in the top speed and maintenance of speed. The utilization of the phosphagen pathway is less explosive here as well (signifying less carryover to the 200m). Also, there's an aerobic component.
You are right, the 200m and 400m were not good choices for what I was trying to say. As you said, the 400m, especially for trained runners, is under 1 minute and therefore primarily glycolytic (for a slow poke like myself, it'll be aerobic at the end as well). And yes, the 200m and 400m are too close in distance and energy systems, so my analogy does not hold for them.
Despite that, the general trend IS correct on both weights and running. Training at a higher intensity has much more carry over to lower intensity work than the opposite. This is why shorter running efforts (interval training, sprinting, etc) help longer distance efforts (1 mile, 5k, etc) much more than the other way around. However, it only helps up to a point: just like heavy bench press has less and less effect as you try for higher push-up numbers, 100m sprints have less and less effect as you try for longer distances (5k, 15k, etc). So to get really good at a specific energy system, you do have to devote time specifically to it.
I believe the argument between bench and push ups is not necessarily an argument of pathway training. You also have to include increase of cross-sectional area of the muscle due to training (bench press induced change), overall cardiovascular capacity (not directly, but it may effect conversion of fast glycolytic to fast-oxidative glycolytic fibers), neural development (which I think is probably one of the more important factors), etc.
I definitely agree that there are other factors involved besides the energy systems. For example, in the running example, longer distance efforts (ie, which give you lots of time to practice) may improve your running technique, which help both long and short runs. Having said that, from personal experience, I think the energy systems do play a large role here. When I used to do solely strength training (ATP/PC) and jogging (aerobic), I was piss poor at high rep efforts. I could bench and squat over 300lbs, but couldn't do more than ~40 consecutive push-ups or air squats. Since I started Crossfit, which does a better job of training all the energy systems, I have gotten way better at high rep training (80+ push-ups even though my bench press has gotten
weaker, 100+ air squats). And I don't think it is purely a matter of just having more practice with specific exercises: my high rep abilities have consistently improved across the board, even on exercises I rarely do, such as box jumps, wall ball, back extensions, knees to elbows, etc.