In general, I hate arguments which try to attribute some grand philosophical error to their opponents. On the other hand, intrinsic theories of value really do seem to be part of "folk theories" of economics, were held by lots of smart economists (including Smith, Ricardo and Marx) for centuries, and really are wrong. (See http://en.wikipedia.org/wiki/Paradox_of_value if you disbelieve that last part.)
Katja could have been a little more clear in this article that the propositions she criticizes (such as "When two people trade, one of them is almost certainly losing") could have other supports besides a notion of objective value, so that she isn't so much debunking them as removing one reason to believe them. Still, I think she is right that they derive a large amount of their intuitive support from unexamined notions of intrinsic value.
Also, I think that people are improperly objective about many more things than economic value. "Offensive", for example, is another concept where I think any serious analysis requires it to be a two place function of thing and agent but is usually naively taken to be a one place function of thing.
Finally, let me give the best argument I know against the subjective theory of value. Namely, that the objective theory of value is occasionally false, but (the argument supposes) it is generally a very good approximation because people's subjective preferences don't differ very much over the vast majority of goods. For example, one situation in which I wouldn't blame people for holding an objective theory of value is when everyone is at subsistence levels of poverty, where any deviation from strict calorie cost benefit considerations are lethal.
I called this the best argument against subjective values, but I think it's just empirically wrong when it comes to the modern world, where we are lucky to have a wide range of goods (broccoli, books, bikes, ...) that different people correctly put starkly different subjective values on.