Actually no, but have tested it now.
Pin 1 pot - Ground
Pin 2 pot - LCD pin 3
Pin 3 pot - +5 V
Black boxes on 2nd line, disappear after short time and then boxes on both lines. Turn pot to left for higher contrast.
Pin 1 pot - +5 V
Pin 2 pot - LCD pin 3
Pin 3 pot - Ground
Same as the first as expexted, only turn the pot to the right
Pin 1 pot - Ground
Pin 2 pot - Ground
Pin 3 pot - LCD pin 3
This is how I read your circuit but I might be wrong.
Black boxes on 2nd line, disappear after short time and then boxes on both lines. Turn pot to left for higher contrast.
Using a 10K pot, tryed with a 2K pot with no differense, do not have a 20K pot for testing.
From the potmeter datasheet:

Edit:
When looking on the picture of your working circuit it looks like the LCD is connected to pin 15 and maby 16 of your PIC, is this correct?
(yellow and brown wire, instead of 12 and 13 as in the drawing.)
Migth be wrong but it looks like it when I zoom in on the picture...
Have tried to move the wire from pin 12 and 13 to pin 15 and 16 of the PIC and changing letters appear on the LCD.
It is not correct viewed on the LCD, but at least it shows random letters.