Actually, I had this same issue and I think changing the Theme setting did solve the problem. The underlying problem is that the PPT Theme is interfering with and overriding the appearance of the background color of slides that use images in the background. And the reason why "Format Background" has no effect on the gray background is that that there is nothing actually wrong with the background itself, but only the appearance of the background due to the PPT Theme.
First, it should be noted that my PPT deck used a template that had a background with a PNG image, which had transparent areas that allowed the background behind it to be visible. This PPT Theme problem specifically affected slides that had a background image, but not slides with a solid background color or slides with a background image that covered the entire slide with an opaque image.
For my deck, all of my slides appeared normally on my primary computer. However, on a secondary computer, the same slides had the gray background issue, even though the design themes and color palette remained the same. By changing the PPT Theme on my secondary computer from "Colorful" to "White", the abnormal gray background was removed and the slides appeared as they should - all of this was done without changing the actual color or image used for the slide background. When I changed the PPT Theme to "Dark Gray" and "Black", it changed the slide background to dark gray and black.
I would go so far as to call this a bug in PPT. The PPT Theme should control the color and shading of everything in the application except for the slides themselves. However, it appears that (for Office 2016), the effects of the PPT Theme also bleeds into the appearance of slides, specifically slides with background images.
This is a partially correct description of the problem. I would not call this a bug, nor a "bleed" of the theme. It actually works as designed. Yet, it causes confusion because of the difference in how PP displays the edited slide and the thumbnail views. It could be simplified into the following:
The Office Theme sets the background of the PP application to a different color than white (for example grey). When transparency is used in the background of a slide, we see this grey background of the aplication when editing slides. Yet, when the presentation is being played (F5), the transparent background of the slide is always displayed as white by default. Similarly, the transparent background is being displayed by default as white in the thumbnail preview.
An intuitive solution is, when editing the slides, to include an option for users to view the transparent background as it is going to be actually diplayed when we run the presentation (i.e., white whenever transparency is used). In basically all graphic design software I am familiar with, this is named somewhat like "display transparency" option. The problem affects and confuses people only when they are editing the slides. When you can imagine that any transparency will be displayed as white in the final product, you will not be confused. Of course, you first need to understand how transparency works, which I hope this post will help you with :)