The slow walking tapping into fat stores is kind of misleading. Basically your body burns different percentages of types of energy based on what is easy and what is available. When you are sleeping, your body burns a higher percentage of fat than when you are walking around. Same is true for if you are walking slow versus walking fast/doing intervals, your body is burning a higher percentage of fat but in the same time period will burn less calories overall and less fat overall. Intervals are actually a great way to burn a lot of calories in a short period of time.
If a slow walk is what you can do, then go for it
If you can add in some faster walking intervals into your slow walking, then that will help you burn more fat/calories overall.