I was playing around with QGIS yesterday and today to see what might be happening to prevent it from working. I have not yet discovered why QGIS doesn't work with our server (ArcGIS does seem to work), but I do have a work-around so that you can load the images into QGIS indirectly.
If you use your web browser to view the image, then download the image from your web browser onto your computer, you can then load this image into QGIS. It is not as convenient as having QGIS do it directly, but at least it can work.
So, for example, I entered the following URL into my web browser:
My browser displayed an image with red squares for each fire. I then right-clicked on the image and saved it to my computer. Then I went to QGIS and selected Layer->Add Raster Layer and used the file dialog to select the file I had just downloaded. QGIS asked for the coordinate system, which is WGS-84 (which corresponds to EPSG:4326) for this particular example, and it then displayed the image in its layer view.
If you edit the URL in your browser, you can set your date, time, region of interest, and image width and height for the image you want to download. For example: