The rules say (concerning placing Irrigation)...
"Irrigations are placed on the border of two plots..."
This seems to imply that an irrigation stick CANNOT be placed on the edge of a single tile (i.e., there MUST be two plots and the stick can only be placed between them). I have watched a few play-through videos and noticed that (in some of them) the players were putting irrigation at the edge of a single tile.
We've always played as the rules state. Only if it can be placed in between two plots.
Never on a single plot.