The quick assumption would be that it looks white, but it isn't actually pure white (255/255/255), and the printer is printing it out much darker than it appears on screen. DTG said their values were also fine however, so that couldn't be it there.
The suggestion of making it transparent is probably your best and easiest bet, if you do indeed have pure white. If the magic wand tool won't work well for a complicated design, you can also use Select->Color Range to select all the white in the picture, and then delete it (thus making it transparent). Also note that you can't make it transparent if it's set as the background layer -- which is easily solved by making a copy of the layer, and getting rid of (or hiding) the background layer.
Finally, another thing that might be worth trying is to simply save the finished design as a PNG (or tiff, but png is smaller) and print it from a different program. I do this anyway because it's easier for me - I don't have to wait for Photoshop to load when I want to print something; I just print it off from
Irfanview.