She's wrong. "Industrially" is an adverb, and adverbs modify verbs, adjectives or even entire sentences. The word as used here modifies "nations", which is a noun, and so should be an adjective. "Industrial" is indeed correct here.
Google agrees. A search for "industrial nations" (including the quotes) returns over half a million pages; a search for "industrially nations" (including the quotes) returns one solitary result, and in that result, "industrially" is the end of one sentence and "Nations" the beginning of the next. In other words, nobody else uses the phrase "industrially nations".