wIGG- My FIL used to cook venison steaks that same way, although I don't believe I've ever had backstrap done that way. It is very good.
I cooked a venison backstrap on the grill last year. I left it whole, with Kosher salt and pepper, and grilled it to medium rare. It was absolutely delicious, and just as tender as can be. I made a red wine reduction sauce with mushrooms to go with it, and almost didn't want to use it the meat was so good on it's own.