First, it doesn't matter how good the rider's biomechanics are if the wrong exercise at the wrong time is chosen. An example would be asking a very green unbalanced horse for a canter to walk transition. No matter how good the rider's biomechanics are, the horse is physically incapable of doing the exercise with no trot steps, and will get frustrated and probably very tense. Many, many different examples could be given of something asked for in training correctly, but at the WRONG time in the training, and we all have seen the ugly result.
Conversely, it doesn't matter if the training exercises are very progressive but the rider's biomechanics are off, and the rider is making something physically impossible for the horse. An example would be, trying to put the horse on the bit using the standard progression of of exercises, i.e. having forward, stop, and large circles with moderate bend, but the rider does not have alignment, tone, and basic straightness. We've all seen this one, with the rider sawing at the horse's mouth and the horse's hind end trailing behind. Again, there are many, many different examples of poor rider biomechanics influencing outcome and we have all seen it in real life, even at the upper levels of riding.
So, where does this leave us as well intentioned riders trying to improve in any discipline? No rider's biomechanics can ever be perfect and no trainer's progression of training exercises/work outline can be strung together exactly the right way every time. However, if the rider is always working on and examining her own biomechanics and as the trainer is very conscious of the progression of training exercises and work, good things can happen. Also, when things go pear shaped, as they will, if the problem solving focuses on whether the issue is a rider biomechanics problem or an order of training/choice of exercise problem, the solution should be much easier to find.