Obviously the instructor I worked with last night knows what he's talking about because, as I said, he is an accomplished fighter.
This doesn't make him an accomplished teacher at all.
During your travels you will encounter different instructors with differing quality. You need to recognise when they are either not the best instructor for you, or when they are lacking competence or run a sloppy studio/dojo.
Both what I was taught and what I've experienced have shown me that you do not straighten the arm fully when punching. I also mention this specifically to students, however I know that they'll eventually find out for themselves why it is important. An example of the injury that occur from this practice can be found here: British Kendo Association: Common Injuries 4: Elbow Hyperextension. To quote:
An elbow hyperextension injury occurs when the elbow is forcefully extended beyond it normally physiological range of movement. There is a little bit more movement available but the ligaments function is to prevent the joint moving to the anatomical range of movement. Movement beyond this will result in a fracture.
The increase in power you may get from the extra bit of travel has a high chance of resulting in an injury that can take months to heal properly.
You also shouldn't straighten the support leg while kicking - in fact I find it impossible to do so. Keeping the leg slightly bent keeps the muscles under load and more able to withstand a strike should your opponent kick it. Biomechanically it can also help at the moment of impact if you still have some extension available in the support leg. Even while in a traditional stance such as Zenkutsu Dachi, the back leg is still slightly bent while punching, and definitely (noticeably) bent while kicking.