Depending on the predicate that follows dochira 
mo, it is true that "dochira mo" can either mean 
neither or both. If the predicate is negative, 
then dochira mo means neither. If the predicate 
is positive, then dochira mo means both. Examples:

dochira mo ii desu = both are good
dochira mo yoku nai desu = neither one is good

---Trebuchet