That seems to be quite obvious to me.
He did state that
The routing would be a lot easier if the LCD's pins were along the bottom, rather than the top.
The word 'routing' means to me he might be creating a PCB, perhaps to fit some case that already exists or is ordered to use.
An answer to the question is:
It's much more likely for you to find a 1602 display that has the pins on the side you desire, than that you will find one that lets you use it in some upside down mode.
This kind of displays has the characters stored in ROM, and has some volatile memory for 8 characters.
This kind of displays has the controller and memory chips soldered to the PCB, without casing.
Those chips are protected by what looks like a blob of black glue, meaning you can't modify it or hack it to do what you like with acceptable difficulty.