I believe your colleague's position is based on the idea that a conjunction should coordinate elements of the same type.
in terms of both [economic (worth)] and [ecological worth]
satisfies this criterion ("worth" is omitted directly after "economic" due to ellipsis, but it is understood).
both [in terms of economic worth] and [in terms of ecological worth]
would also satisfy this criterion.
both [in terms of economic (worth)] and [ecological worth]
seems to either coordinate unlike elements (a prepositional phrase and a noun phrase), or to express an incomplete thought (both [in terms of economic and ecological worth], and [...]).
See the usage note in the "Oxford Living Dictionaries" entry for both:
When both is used in constructions with and, the structures following ‘both’ and ‘and’ should be symmetrical. Thus, studies of zebra finches, both in the wild and in captivity is better than, for example, studies of zebra finches, both in the wild and captivity. In the second example, the symmetry of ‘in the wild’ and ‘in captivity’ has been lost. Other examples: her article is detrimental both to understanding and to peace (not her article is detrimental to both understanding and to peace)
I don't know if there is some other analysis according to which non-parallel use of "both" is grammatical. It certainly sounds acceptable to many native speakers, but that's not an absolute guarantee of grammaticality.