The short answer to your question is obvious: You cannot simultaneously be in an anabolic and catabolic state.
Yes protein can be converted into glucose if carbohydrate intake is insufficient. However, that mechanism is inefficient as is converting glycerol into glucose, which is why fat stores aren't a sustainable long-term substitute. This may be happening in the obese novice who restricts calories though but there are also other adaptations happening as well (e.g. increase in glycogen storage capacity, water retention, neuromuscular efficiency). In my experience with very obese novices, they tend to hit a wall while still carrying high amounts of body fat (i.e. taking a 320 lb obese novice male down to 270 lb. and still obese). Part of this is changes in leverage and part of this is prematurely becoming intermediate due to caloric insufficiency. In short, there are many reasons an obese novice lifts more and changes his body composition while in a deficit, not all of which are fully understood. An intermediate or advanced lifter is going to need to be in a surplus to build muscle and get stronger as a general rule.
Why an outlier can pull it off is beyond me. I added 25 lb. to my 10 RM squat and 5 lb. to my 10RM deadlift after losing close to 30 lb with 24 years of weight room experience, of which the last 10 years were spent training seriously. I lost 9 lb. off my 10RM press though. No idea why that happened but it did.