"one person who is perceived as being a member of that group did something offensive."
Number one - killing someone by beating them, stabbing them and setting them on fire is a bit more than "offensive"!
Number two - being a muslim is a bit more than being "perceived as a member of that group" - they ARE a member of that group. I'm a male - I'm not "perceived" to be a male - I AM a male.
These guys were muslims - they aren't "perceived" to be muslims - they ARE muslims.
Your posting doesn't make much sense.