I just installed Photoshop Elements 13 and opened up a grayscale picture in the Expert editing mode.
I then Clicked/selected File|Print and brought up the print window:
Image 1:

The printer in the Select Printer box (the Zerox Phaser 6180) is not the one I wanted, so I chose my Epson inkjet printer and selected Glossy Photo Paper:
Image 2:

When I go to the bottom of this window and select Print,
Image 3:

Elements Prints to the printer in Image 1 above (Xerox Phaser) and not to the printer I selected. I have multiple printers on my home network, and it doesn't seem to matter which printer I select, Elements always attempts to print to the Xerox Phaser in image 1 above. (Note: I also have Photoshop CS5 installed on this computer and I can choose any printer just fine from that and any other program on my computer, just not Photoshop Elements Ver. 13.)