it would help if you used better adjectives than "safer".
POINT 1: there are more injuries in mma than boxing. that is undeniable. MMA fighters get way more surgeries than boxers.
POINT 2: there is an argument that boxers are more susceptible to getting their brain damaged in boxing than mma, primarily due to the standing 8 count (e.g. if a boxer's bell is wrung, they get a standing 8 count and then keep getting hit in the head, whereas in mma usually when a guy gets his bell wrung the fight ends very quickly)
assuming the 2nd point is true, then does more injuries but less brain damage = "safer"? that's a debate unto itself, but a purely semantic one.
and the 2nd point is far from a fact. it's a reasonable hypothesis, at best. one i happen to agree with.