The question stem asks us to identify an assumption upon which the argument relies. That means we're looking for an assumption that is necessary; if the assumption were untrue then the conclusion would be untrue.
Here, the author is arguing that a good way to tell if an idea is catching in is to monitor the word expressing the idea's passage into private usage.
This argument relies on the assumption that a word's meaning is not severely distorted as it passes into common usage. How do we know? Let's look at the negation.
The negation of answer choice D is "As a word passes into common usage, its meaning does undergo severe distortions in the process."
If the meaning of a word is severely distorted, then the usage of the WORD does not actually reflect the popularity of the original underlying IDEA. The word's meaning has been distorted, so the word itself is no longer related to the idea in the public mind. This would make the author's conclusion untrue.
