A sedentary person will certainly loose fat as a result of starting a rigorous cycling program. They may think they are loosing muscle too, but unless they are starving themselves, I don't see how that can happen. This can be checked by measuring strength.
Cycling "kills" muscle because a competitive cyclist (not your average person out for a recreational ride once or twice a week) is going anaerobic. Simply put, when you are producing the amount of energy we are discussing your body will pull from the easiest source of nutrition, fatty acids and glucose, once that is depleted it will start to pull nutrition form your muscles. Let's say you strength train 2 times per week for 30 minutes each time. You are building muscle which is the act of tearing down the tiny muscle fibers and then they heal and are bigger, now capable of a stronger load in strength. Well, if you go out a cycle for 1-2 hours 5 times per week and your body will eat your muscle once it has tapped out your fatty acids and glucose storages which it will quickly do with that much cardio. Again, we are not talking about the average person that is riding 10-15mph, but someone who is going all out for 1-2 hours at speeds of 16 at the slowest to 30 mph and watts of 150+ (lower watts for women).
You may be building muscle but it is nearly impossible to build it at the rate you would need to do of strength training to keep it on and the amount of protein you would have to consume based on the energy you are using to ride. Most riders also view it from a perspective of wanting to be lighter, the lighter you are the less weight you are carrying. While muscle helps you attain certain goals, too much bulky muscle will hinder you on endurance sports such as marathons, triathlons or endurance cyclists. You want to be lean and effective or what is called economy of exercise. A bulky body builder may be able to hit a sprint hard for 30 seconds to a minute but then he is finished and will struggle in hill climbs because he has so much extra weight in muscle and if you put a body builder on a bike long enough with the rides that are done weekly during training, he will start to lose his muscle within months as well.
So you cannot really say that you would have to intentionally starve yourself but in a sense your body is being "starved" during the anaerobic phases and so muscle is used as an energy source, it is rebuilt and then it is used again and the process continues until there is some type of a change.