Can an at-will employer fire someone for somthing that happend off the clock and off business property?

I was at the scene of a confrontation between two other employees,which ended in one being hospitalized. i then left with the other employee. once word of what happened got back to the employer i was insinuated to be involved in the ault by ociation. i was contacted on my day off at home and informed of my termination without detail of my involvement. i was a fairly good employee with no previous record of confrontation. even being praised as a good worker by my employer during my conversation of termination. i basically need to know in all fairness, do i have any rights?