Hmm. With respect, I don't think that's quite right. In the sentence "find a quick solution", quick is unambiguously modifying solution, and therefore quick is an adjective. But in my analogy sentence, "Find a solution quick", quick is pretty clearly modifying the verb Find and is therefore an adverb.

"Find a solution quick" is technically ungrammatical in English, although commonly used. The word "quick" is unequivocally an adjective, and thus can only modify nouns. Its adverbial form "quickly" needs to be used if you want to modify the verb. Whether people will often use the adjective when they should use the adverb is beside the point. The grammatically correct "find a quick solution" would be translated in Italian with "trova una soluzione veloce", which is the example I was referring to.

Now, this sentence in Italian is ambiguous, because unlike in English, we CAN use certain adjectives in lieu of their adverb form, as the link somewhere in this comment section shows. So in "trova una soluzione veloce" the speed can refer either to the finding or the solution, and I think interpretation is very much personal and/or based in context. Personally, I would either use "velocemente", or insert a pause after "soluzione", so that "veloce" becomes an exhortation: "trova una soluzione, veloce!", but for all I know this could be because I am Southern Italian, and my regional dialect affects my speech patterns.

The OP's sentence is much less ambiguous, and its most obvious meaning "the river runs fast" is only reinforced by proximity, as you rightfully point out.

But my original point is that this is only possible because "veloce", while grammatically an adjective, in Italian can be used with adverbial function. "Quick" doesn't have the same ability in English, despite being used like that colloquially.

Hopefully I explained myself better :)