yea..i'd wear protection for your skin too. just a back protector helps protect you from pwning your central nervous system, but pwning your skin hurts more.
and if you somehow beef it enough to hurt your back, you'll probably be getting potential rash too. so...i'd always wear a jacket. the only squidly thing is the fact that you arent wearing a jacket for protection of anything other than your back.
i think i said that in the most complicated/longest way possible, but that's how i roll.