This is definitely a topic that is one for the digital age, and one that many people have contemplate over, both artistically and technically. As with any argument, there are multiple sides and it all depends on your personal opinion about what constitutes processing of a digital image. Of course, the term processing has changed when we left chemical processing (a mechanical process) for digital processing.
First, realize that in film days ALL photographs were processed. You could not make a print without processing the negative. The precursor of today's digital processing, or digital editing, primarily occurred during the printing process. That's when images were blended, dodged, burned, cropped and what have you. This allowed the photographer to get creative with his vision for his image. In those days one could distinguish between the act of processing with that of image manipulation.
Keeping that separation in mind we can therefore think of a digital photograph as being processed (in camera) by the camera's onboard digital processor that converts the raw data from the sensor into a visual image. That digital image is processed according to predetermined settings you apply during your initial camera setup (color space, image style, aspect ratio, etc.)
Then, if the image isn't to your liking, you can bring it into Photoshop in order to manipulate (post-process) the photograph to closer resemble your artistic vision. What level of manipulation you give the image is dependant on what you want the image to say to your audience. Is it a quick snapshot? Is it a representation closer to what you initially saw? Perhaps it's an enhanced portrayal that brings out more of the beauty than what was there. Maybe it's a combination of multiple images in order to create something that wasn't there but rather something that was in your mind.
On a basic level, most photographers will argue that every image that comes out of a camera should be processed, sometimes called normalizing or balancing an image. In this case the manipulation is kept to a minimum and is looked upon as correcting issues in the image due to the limitation of the camera (after all it is a machine and will never capture what our eyes see.) These modifications usually consist of exposure fixes due to either human error or lack of dynamic range of the camera, cropping, straightening, color correction and lens perspective correction.
So, in short, your question should read, "is photo manipulation cheating?", rather than processing because, by default, all cameras must "process" an image.