The value a person places on a good is not “based” on money, but expressed against the value he places on money. If I value an iPad more than I value $500, then I gain if someone sells me an iPad for $500. The seller must also gain by the trade, i.e., he must value $500 more than he values the iPad, otherwise he would not trade. If there is another person who values the iPad more than $400 but less than $500, then we can conclude that if the seller sells to the first buyer instead of the second buyer, the iPad has been allocated to the person who values it the most compared to money.
If people do not use money in trade but whatever barter goods they happen to have, then it cannot be determined which of the buyers values the good he has to sell more than another. One offers two beaver pelts for the iPad and another offers a chord of wood. The seller can tell which offer by the buyers he himself values more. But which buyer values the iPad more highly is indeterminate.
Labor, also, cannot be used to determine who values something more highly. The units of labor are different from person to person. If one person values the iPad for 6 hours of his labor and another person values the iPad for 12 hours of his labor, nothing can be inferred about which person values it more. The different units of money, however, are homogenous. So it is possible to say whether one person values something more highly relative to money compared to someone else.