Is it feasible to cook a gourmet tasting menu in a home kitchen?
I agree it's quite believable. Most restaurant equipment is more about cooking in bulk than being particularly specialized things you can't get at home. So it's extra durable/stays sharp longer or is just big (like a fridge). 

It really doesn't take much money to make good food though. A lot of the gadgets and gizmos that you see on TV can be replaced with 1 good knife kept sharp...and a lot of chefs prefer a knife for the control. For example I have a mandolin. It cuts my vegetables very rapidly and saves me a bunch of time when I make vegetable stew, which I make a lot-- but it doesn't cut my vegetables evenly, which in a gourmet restaurant could be a problem for presentation. (Actually I'm going to get rid of my mandolin soon, too. I've gotten faster with a knife by now from practice.) 

Another thing to think about-- being a chef is a hard job. If you're a gourmet chef you're probably passionate about cooking, so it makes sense to spend money on that hobby for at home as well.