im wary of everyone jumping to conclusions here.
theres very little detail given on how the saw came into contact with the finger.
sounds like it is one or both at fault, but not enough detail to assume who.
could be that one reached into the cutting zone, could be the saw jumped, could be the saw was swung carelessly. usual practice is stay away from the big noisy sharp cutty thing.
5m distance is standard guidelines from what i know, but i think is a little tricky in a domestic setting
a physical barrier between workers seems excessive, anyone on site should know the safety principles or shouldnt be on site.
sadly it does usually come down to operator behaviour at fault. but some wise-ass will always turn it onto management and it becomes their fault for not enforcing procedure.