Its called educational validity, building from simple to complex and following a proven system. I am a PADI Instructor and often add more practice and techniques (the standards manual says that students must be able to demonstrate the skill in a comfortable, fluid repeatable manner to prove mastery and meet the performance requirements but unfortunately many Instructors in all agencies don't follow this definition) but don't agree that Instructors should be allowed to add extra skills. This could cause task loading and of course there are a million situations when it could or could not be appropriate but leaving that in the hands of so many instructors, with differing skill/experience levels and judgement, I could see that being hard to defend in court if something should happen.
I'm unsure what you mean by the tables being liberal. They were designed and extensively tested for use by recreational divers instead of the Navy Tables used elsewhere, designed primarily for fit young men doing decompression diving. The spencer limits 60 minute washout model employed by many computers is the same model as the PADI table. PADI tables give shorter dive times for single dives but becuase they use a shorter surface interval credit (60 minutes instead of 120) they give more time on repetitive dives. Out of 2,000 dives i've never seen anyone get bent diving within the table limits even when they have other pre-disposing factors.
To me, all systems have been proved valid and I don't think anyone can say who does it better than the others as we all have our bias but as a dive center manager I don't think of any one certificationc card as being more acceptable than another and really believe it mostly comes down to the instructor that you had; their experience, comprehension and application of the tools that the agency puts at their disposal and personal passion, methods and personality.
