The top hits on a Google search will tell you definitively: no, muscle does not turn into fat. It's sort of true, but it's not that simple.
Your muscle is always being broken down and built back up, using amino acids as building blocks. When you're weight training, there's usually more synthesis than degradation going on, so your muscles grow. When you stop exercising, there's more degradation, so your muscles atrophy, releasing amino acids back into the blood stream. There are also amino acids from your diet in your bloodstream (dietary protein is broken down into amino acids before being absorbed). The amino acids in the bloodstream can have a couple different fates:
- Typically, they will go towards building protein in the body (almost everything in your body is made out of protein).
- If you don't have enough carbs or fat in your diet to meet your energy needs, amino acids will be used as fuel.
- If your protein and energy needs are met and there are still amino acids left over, they will be converted into fat and stored. The specific amino acids that are converted into fat may have come from the diet or they may have come from muscle atrophy--they're all in one pool once they enter the bloodstream.
So it's not like your six pack morphs into a beer belly, but it's possible for some of the protein from your muscles to be converted into fat (perhaps elsewhere in the body), if you're eating more protein than you need. However, you can see how saying it's a "slow decrease of muscle through lack of use, and increase of fat through bad eating habits" is a pretty accurate simplification.