"a reference dimension is usually shown without a tolerance" is what i learned in gd&t class. a basic dim's tolerance is found in the fcf.
A reference dimension is always shown without tolerances. A basic dimension is exact, and has no tolerance, as it defines perfect geometry. Tolerances are for features (either size or location), features are located from datums by basic dimensions.
My cad software lets me create reference basic dimensions, but I don't trust it to be right, and have only been forced to use such a critter once (and cringed even so)...but nobody has questioned it, and that particular drawing has gone overseas and back. Have not seen the subject of referenced basic dim's. discussed by the spec, nor by any authoritative guru (i.e. somebody not posting in this forum).
I will point out, again, that repeating a basic dimension may be over-dimensioning, but since basic dimensions ARE EXACT, there will be no difference between parts made with multiple basic dimensions, or parts made with a single basic dimension, locating the same feature (provided there isn't a conflict in the value of the dimensions). To be certain that people know what you mean, perhaps adding "REF." adjacent to the basic dim. block, instead of the parentheses, would make it clearer. You could even say "REF., see Sheet 1" or similar.