It IS the reason.
When the forearm joint is placed closer to the wrist,
When you say "forearm joint" which joint are you refering to? Your elbow?
it creates a fulcrum more capable for supporting a weight.
There is actually two different axes of rotation (fulcrums) here your elbow and your shoulder. In this case the force of the weight is acting, roughly speaking, directly in line with your elbow so forearm length has no real impact in this regard. This would come in to play if you were trying to curl the weight, not bench press it. It's actually your upper arm length which matters here.
In actuallity less work(physics) is performed since distance travelled is shortened than someone with a different placed joint.(longer forearm)
This part is partially correct. Someone with shorter arms will perform less work than a long armed person when bench pressing because the weight travels less distance but the joint placement part is off base. Two people with the same length of arms using the same width grip will have the same range of motion, no matter where the hell their elbow is. This is just common sense.
Based on this post anyone with any background in physics or biomechanics would be able to tell that TA is talking out of his ass. Saying anything with great conviction will convince most people, even if it is a crock of shit.