The hip flexors do not cause initial hip flexion.

The hip flexors are not responsible for pulling/flexing the swing leg forward in gait or running. The psoas is a mere swing phase perpetuator, not an initiator.
For about 2 decades we have been saying in our lectures, posts and podcasts that it is the reduction of the obliquity of the pelvis during gait from various other tissues and biomechanical events that causes leg swing, meaning the trail leg is brought forward in swing largely by the abdominal muscle linkage to the pelvis (and other loaded tissues) that is responsible for forward swing of the leg. It is not the hip flexor group that does this hip flexion action. Thus it could be considered foolish to train the hip flexors to be the primary swing drivers. Here is another supporting piece of research.

"These experiments also showed that the trailing leg is brought forward during the swing phase without activity in the flexor muscles about the hip joint. This was verified by the absence of EMG activity in the iliacus muscle measured by intramuscular wire electrodes. Instead the strong ligaments restricting hip joint extension are stretched during the first half of the swing phase thereby storing elastic energy, which is released during the last half of the stance phase and accelerating the leg into the swing phase. This is considered an important energy conserving feature of human walking. "

Dan Med J. 2014 Apr;61(4):B4823.
Contributions to the understanding of gait control.
Simonsen EB1.

https://www.ncbi.nlm.nih.gov/pubmed/24814597?fbclid=IwAR3yZQLb2Z0X1LZSVp2hOFLCt3wefsPt4iWEGveswn7-aGaou5OdDqmj4lA

So, what attaches to that hip capsule anyway....

I was trying to figure to which muscles attached to the labrum of the hip, as I see many folks where theres has gone south. I had always wondered if the iliopsoas attached, since many people with labral pathology have hip flexor dysfunction, where they use their psoas and iliacus as hip flexion initiators (or sometimes the rectus femoris, TFL and sartorius), instead of the abdominals. It turns out that NO MUSCLES attach to the labrum, but some attach to the capsule. 

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Have you noticed that many of the muscles on the list below (not the obturator internus) are internal rotators AND work during the 1st part of stance phase? Remember "glide and roll"? With internal rotation of the hip comes posterior translation of the femoral head. If these are dysfunctional, you may get capsular "pinching". Think about it with the next patient with hip joint pain from initial contact to midstance. 

"An updated knowledge of the intricate relationship of the pericapsular and capsular structures is essential in guiding our treatment of the hip. Following dissection the authors were able to discern that the iliocapsularis, indirect head of the rectus, conjoint tendon (of the psoas and iliacus),  obturator externus and gluteus minimus all have consistent capsular contributions whereas the piriformis did not have a capsular attachment."

 

Walters BL, Cooper JH, Rodriguez JA New findings in hip capsular anatomy: dimensions of capsular thickness and pericapsular contributions.
Arthroscopy. 2014 Oct;30(10):1235-45. doi: 10.1016/j.arthro.2014.05.012. Epub 2014 Jul 23.

Psoas, iliacus. . . .  hip flexors ?

How many times have you heard us say, “hip flexion in the swing phase of gait is not driven by the hip flexors. In swing phase, the psoas and iliacus complex is not a hip flexor initiator, it is a hip flexion perpetuator/” ?
More evidence … . .
“These experiments also showed that the trailing leg is brought forward during the swing phase without activity in the flexor muscles about the hip joint. This was verified by the absence of EMG activity in the iliacus muscle measured by intramuscular wire electrodes. Instead the strong ligaments restricting hip joint extension are stretched during the first half of the swing phase thereby storing elastic energy, which is released during the last half of the stance phase and accelerating the leg into the swing phase. This is considered an important energy conserving feature of human walking. ”

http://www.ncbi.nlm.nih.gov/pubmed/24814597