It's not that you don't get to see how our SFs conduct their drills. There are more than enough videos from exercises like Vajra Prahar that show how we do it.
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Even a cursory look would tell you what all is outdated by several decades here. These stances were used by Western SOF in 60s through 80s. Nobody leans forward (the guy in front is actually throwing his weight back), nobody puts their non-dominant side leg forward to get into a more balanced stance (try it out yourself, stand like that and ask a friend to push), nobody uses a thumbs-forward grip (maximizes contact of non-shooting palm with grip, minimizing muzzle flip) and instead some are using the old "cupping" grip while others the thumbs-crossed grip...even in that there is no standardization...in the pic you can see each Para commando is holding the pistol a different way.
Some examples of correct 'modern' stance & grip:
Even Russians adopted the same:
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At least IAF Garuds seem to be experimenting with some modern methods, though it seems far from standardized:
Even CISF VIP Security units are ahead in that regard: