Harris is arguing that, if we begin with an axiom (which Outhouse has correctly identified, in Harris' case, as "the [aggregate] well being of conscious creatures"), then science through the establishment of fact, can in some cases determine what values are logically consistent with the axiom. Harris' position in no way, shape, or form requires all humans to have precisely identical values.
In fact, Harris argues that, just as there are different foods that are healthy for us, there are likely to be different values that can be logically derived from the same axiom. That is, Harris foresees a diversity of values, rather than single set of values.
Last, Harris explicitly rejects the notion that getting everyone to agree on a set of values is necessary or even desirable. To Harris, that would be like the notion that everyone, including the village idiot, must agree on string theory in physics for string theory to be considered true or useful.