I would be skeptical as well, however the Tesla is very easy to check. From the top link on Google:
"[the range of the Model S] 85 kWh battery pack is 265 miles"
86,000Wh x 3.41 BTU/Wh / 265 miles = 1107 BTU per mile
I'm going to say that their claim is "accurate" based on a very simplistic level. As you point out, there are efficiency losses in generation, transmission, and charging.
Now, if you use the EIA rates (http://www.eia.gov/tools/faqs/faq.cfm?id=667&t=3) for power generation, it's more like 10 BTU/Watt, which puts the tesla up to 3300 BTU per mile (ballpark), and still doesn't include transmission or charging losses. Of course, whether you're burning coal for that 10BTU or allowing fissile decomposition for that 10BTU makes a pretty big difference in the type of pollution you're going to have as a byproduct. (that's another argument, of course).