It's a good discussion here.
I think the main thing is training to meet your actual goals. The question on LSD that was posed has no goal-specific context, which is why so many different perspectives are being thrown at it.
To put it into goal-specific context - if you do not train for long distance events there is absolutely no need to do long slow distance training. You can do easy rides and hard rides in your training cycle, but no need specifically for long and slow rides.
However, if you do significantly long distance events, then longer slower rides become a necessity - for many of the metabolic and physiological reasons already outlined above, but also because you need to get the body accustomed to a comfortable and sustainable posture which will allow you to get through very long rides. If you don't have that acclimatisation you could easily have the fitness to ride the distances, but you will not be able to last in the actual event, due to 'comfort issues' and possibly even injuries.
There's a 3rd possibility, which is that an individual rides regularly and often, but never particularly long distances. However, the total number of hours spent riding are significant. In such instances a person could well be spending enough time practising sustainable posture that the need for lots of long slow rides to establish this postural efficiency becomes unnecessary. In such cases sticking to intense training can probably do the job of preparing such athletes even for a very long event. However, there will still be a requirement for a small number of long distance 'practice runs' so that you know what your actual long distance pacing and riding strategy is.
One last thing: that popular "fat burning" issue is worth addressing. Physiological studies clearly show that a higher PERCENTAGE of your energy is derived from fat burning when you ride at an easier and more sustainable pace. However, MORE TOTAL CALORIES are burned when you train intensely and although the percentage derived from fat burning is lower - the TOTAL AMOUNT OF FAT burned is higher for intense training.
Basically, fat is harder for the body to access than carbohydrates and cannot be accessed fast enough to sustain very vigorous activities. Fat burning is useful only for slow-burn activities. But intense activities need as much TOTAL energy as possible and will draw on all available energy sources in order to keep the body going.
Here's a totally hypothetical example to demonstrate the calculations being described above: If your body can access, say for argument's sake, 100 calories per hour from fat during slow riding then it will possibly be drawing about 200 calories per hour from the fat stores under very intense exercise. THAT'S DOUBLE. But for the slow riding 100 calories per hour may be over half of the total calories burned. For the intense riding 200 calories of fat burning may only be one fifth of the total energy burned.
In the above scenario, there is a greater PERCENTAGE of the energy derived from fat in the slow ride - but MORE TOTAL ENERGY derived from fat in the fast ride. That is the reality of how the human body works.
There is still one more important aspect to the 'fat burning question' - that being the so-called "after burn" effect mentioned, which is a raised metabolic level causing more calories to be used by the body when at rest (and often for more than a day after the intense training session has ended). Compare this after-burn effect to a 5 hour ride. In a 5 hour ride you will need to eat regularly in order to keep going. That makes the ride somewhat CALORIE-NEUTRAL - because you put in as much energy as you are burning (or else you will 'bonk'). So long rides are not the best way to train if you want to burn fat, they are calorie neutral and you make up for the energy burned by eating more as you burn that energy. You do not need to eat as much to sustain a really intense session and most people wont eat at all during a very intense session, only before and after. Compare that to the amount of food eaten in a long slow ride.
So long slow riding is essential for training for endurance events - and will allow you to become more efficient in burning fat for slow-burn energy - but intense training is better for losing fat from your body and getting leaner. It also gives you better fitness per hour of training time. This logic applies to EVERYONE (and that anecdote about the BBC documentary stating that intense training only works for specific genetics is not accurate). Specific genetics allow you to continue to improve your ability to use oxygen though interval training but everyone burns more fat by doing intense intervals.
Because the BBC guy is more of an academic than an experienced fitness trainer he didn't contextualise the genetic information for athletes to understand and rather just focused on his personal interest and scope. The actual "genetic" concept being referred to in "athlete language" is the same as saying "some people are sprinters and others are endurance athletes". If you have those genetic traits you cannot change them. This does not mean sprinters cannot train successfully for a marathon - it just means they will not respond to the training as well as the endurance athletes will. Everyone can burn more fat by training specifically to do so - and everyone can become fitter through appropriate training - it's just that genetics determine to what extremes these developments can eventually go.
I hope that's a useful perspective?