Radioactive, welcome to the DamageControlMMA forums. Thank you for asking your questions here so that we can all benefit from each other's perspectives and experience.
I offer my opinions in this post but by no means should you take this as a definitive answer.
In my experience I have come across numerous contradictory theories and ideas concerning tactics, techniques and training methods. Not only have I encountered these contradictory ideas, but they have usually come from instructors at the highest levels with equal experience and expertise on the sides of each party.
What I have taken form these contrasting vantage points is that there really is no right or wrong way. If you can understand the reasoning behind why each instructor says to do it one way as opposed to another then you've really learned something. From that point on, you can make your own informed decisions based on how the different philosophies relate to your own, and how the different techniques relate to your strengths, weaknesses, temperament, and body type.
For example, I have heard Royce Gracie say that you should shoot a takedown by lowering the rear knee to the ground first before you drive in for the shot. I have heard Sean Sherk say the opposite, that when working a shot, you should lower your front knee to the ground first.
To hear these two methods and to focus purely on the technique could definitely be confusing. But when you step back and listen to their different contexts, things begin to make more sense.
Royce explained that his art is primarily a self defense art. That Gracie Jiu-jitsu was developed to defend a person on the streets. There he said, there are no soft mats or cushioned surfaces. If you put your front knee down first, he said (and I'm paraphrasing here), you will hurt your knee and maybe even injure your leg.
Sherk on the other hand was coming purely from a sport background where his takedown was specialized for the ring/cage/mat and optimized for the maximum amount of speed and power based on the environment he would be using his tool in.
Which was wrong and which was right? I'd say neither and both respectively. I have students who intend to use their art in combat sport, I have others who study primarily for self defense. I have the benefit of learning from two experts in the field of Martial Arts and I can give each kind of student the information they need to choose which method best suits their game and philosophy. Some may use one because they sport fight, others may use the other because of their self defense mentality, and still others will be able to switch depending upon the situation because they know which tool is best suited for the particular job.
As for the bent knee and the straight legged approach to the straight right/right cross, I'm not going to pretend to know why each of the instructors you've seen would do it one way over another. The best thing to do is to respectfully ask. But, from my humble experiences, I've been taught that the bent knee helps you to "sit down" on your punches and increase your power by lowering your center of gravity. I'm not certain why one would keep the leg straight. My unsolicited guess would be that it has to do with kinesiology and trying to create a pike of bone that runs from the ground up the shin bone, through the femur, up the spinal column and down the arm to increase the efficiency with which force is transferred from your body and into your opponent's.
I apologize if my attempt at answering this question is unsatisfactory. I know that simple black and white answers are always easier to swallow. I know that that's what I always wanted. But the more I begin to understand the nature of this enormous beast we call the Martial Arts, the more I feel that there are very few black and white answers if any.
Best of luck and thank you again for your support!