Sentence Correction

The exercise asks you to indicate whether or not the underlined portion of the sentence correctly modifies any word(s).

The patient's rare disease was treated using novel techniques developed at the medical school.

My question is regarding the solution:
The underlined portion is incorrect since there are no noun(s) in which "using novel techniques" modifies. According to MGMAT, one of the ways to fix it is to change the underlined portion into a prepositional phrase, as in:

The patient's rare disease was treated through the use of novel techniques developed at the medical school.

However, "through the use of..." is a prepositional phrase that serves as a noun modifier, and the main subject that it is now modifying is "rare disease". Doesn't this destroy the meaning of the sentence? The sentence is now stating "the use of novel techniques..." is somehow modifying "disease," when instead "through the use of.." should modify the way the disease was treated. Wouldn't it be better to use a verb modifier instead to modify the way the disease was treated? As in:

The patient's rare disease was treated by using novel techniques developed at the medical school.

Now the verb phrase, "by using..." correctly modifies the way the "rare disease was treated."
Anyway, please help me out here. Thanks!