I don't think you are missing anything.
While your suggestion would seem to work electrically, I'm not sure it is possible mechanically.
There isn't much space once the shield is plugged on to the Uno and the pins are quite stiff in terms of bending
so I'm not sure you could make it fit/work.
The other h/w solutions in the thread are electrically the same as what you are proposing,
they just tap into the circuit by modifying the traces on the PCB rather than mess with the header pin.
I'm using the SaimSmart 1602 as well but I'm not putting it right on the board, instead using DuPont cables to connect all the necessary pins to my arduino. I apologize for such a simplistic question, I believe it's basically the same as the last one you got, but it would work if I put a resistor in between digital port 10 on the arduino and the equivalent in the LCD shield?
If so, what resistance should I use?
And to be clear, I'd like to be able to use PWM control to dim the backlight, but I really don't want to physically modify the board if I can modify something outside (especially since I already have room to put stuff between the pins).
Again, I apologize for my simplistic questions. I'm not an idiot when it comes to electronics, but this is sort of my first dive into this sort of stuff.