I think it is reasonable to suggest that the good Earl invented the culture of the Sandwich, and not the concept of meat served on or between a peice of bread.
However, it is the culture of the sandwich which has elevated the sandwich to such an important position in the deitary habits of the world and most especially in America. The real difference between the Earl's sandwich and all the food stuffs that come before it is that the Earl's sandwich was meant to be eaten while doing something else - most importantly in the US - while _moving_ (walking, driving, whatever). That distinction is most easily seen in the difference between the way Europeans and Americans normally eat thier sandwichs. If you are cutting up your Sandwich with a knife and fork, it might look like a Sandwich but it isn't culturally a Sandwich.
The idea that the eating of food would be of secondary cultural and personal importance to the accomplishment of something else is a rather novel idea I think. While there were certainly street vendors offering food wrapped in flatbreads or on split rolls in various civilized (and by that I mean the literal meaning of the word) corners of the world prior to the Earl ordering the kitchen staff to bring him his meal wrapped in bread so that he could keep his cards clean, I don't think it was a ubiquitous cousine of any social importance.
Now, in America, it is absolutely inconcievable to imagine life without sandwichs and meals when you actually sit down and sup with people and take ones time in enjoying the meal itself are rather rare.
And, as fungasite point out, there are alot of inovantions involved in the production of a sandwich as we know it, so if you want to get really strict about the definition of a sandwich you might well say that the Earl invented it. Certainly his colleagues seemed to find the activity novel enough that no other word suggested itself for the dish, and it was remarkable enough that they felt the need to identify it.