The second part of this trigger control theory is that it's important to "pull the trigger straight back." Well, the trigger only goes straight backward and straight forward; there is no other way to pull it. If the trigger on your handgun goes in any other direction than backward or forward, have your armorer take a look at it because something is wrong with it.
The other problem with this theory is that your finger does not work like a hinge. It doesn't go back and forth, it curls. The problem is that the phrase to "pull the trigger straight back" is used to teach the all important trigger control theory.
Tons of time and paper have been wasted on teaching and writing about "trigger control." Let me ask you this simple question. Imagine I take your handgun, line it up on target on the range, and lock it into a heavy metal vise attached to a heavy steel and wooden table which is bolted into the concrete floor. Once I've secured the gun so that it can't move, I attach a piece of string to the trigger and slowly pull the string until the round goes off. Where will it go? If you said straight into the target, you are correct.
Now instead of slowly pulling that piece of string attached to the trigger, I jerk it as hard as I can. Now, where will your round go? Again, if you said it goes straight into the target, you are correct. Where else could it go but into the target? So what's more important: how you pull the trigger, or how you grip the gun? Obviously how tightly you grip your gun is going to be more important.
One of the arguments that some firearms instructors bring up concerning this topic is, "Ask a sniper if trigger control is important." Well, if you think that a sniper firing a round out of a rifle from 300 yards away is under the same survival stress as an officer who is getting shot at from less than five feet away, then you should rethink your position as a firearms instructor. We need to train the way we fight, and that is to have a tight, convulsive grip on the firearm, and not worry about "trigger control."