I've been cycling several thousand miles a year for many, many years, and in my experience I can certainly "outrun" a bad diet. Go for a 40 mile bike ride 5 days a week and you'll have a difficult time eating enough food.

A couple years ago I added weight lifting to my regimen and I could never eat enough. Most days of the week I'd stop by mcdonalds to pick up a couple mcdoubles as a snack. I was easily consuming 4-5 thousand calories a day (150-175 grams of protein) and I was still losing weight while gaining muscle. At one point I was sub-10% body fat whilst eating a mix of healthy food and junk food. Every visit my personal trainer was telling me to eat more.

If you're interested in losing weight while eating whatever you want I suggest doing 10-15 hours of fairly intense cardio per week, and 2-3 very intense lifting sessions per week.