there could be many explanations for this strange effect and this is the type of stuff Dr. Jacob Wilson likes to study, namely the various anomalies in the body's response to both food and training ... but i'm not sure we as dilettantes should focus on odd effects like this or at least we shouldn't try to extrapolate them to general rules from a single anomaly ...
we know a body has a set point for fat mass for example - that is if you have unlimited food you will reach a certain weight and stop getting fatter.
there also appears to be a similar set point for muscle mass as well, regulated by myostatin. there was at one point an attempt to use myostatin inhibitors as super drugs for muscle building - not sure what is the status of that now.
what may have happened in this experiment is during fasting the participants dipped below their set points for both fat and muscle but were able to rebound muscle mass faster than than fat mass. if that is the explanation then there was nothing about this unique to fasting itself.
BUT it could also be some unique effect of fasting. it could be that fasting primes the body for muscle building later when protein is reintroduced into diet. i don't know.