As a linguist I would say the claim of correctness is applicable if and only if it is derived from common usage. The native speakers of a language themselves decide what is correct or incorrect via their usage of the language. It is for this reason that a language can be said to be “alive.”
There exist certain grammatical rules derived from Latin which were unsuccessfully imported into the English language in the mid-1800’s. These rules, including “no split infinitives,” and “no ending a sentence with a preposition” have never taken hold in English, and would serve only to reduce the viability and flexibility of the English language in its efforts to express a universe of thought. English stylists, and grammarians are largely disenfranchising such rules upon consideration that they have no bearing in any real-world dialect of English.
Any time you use an existing English word modified by legitimate grammatical practices, and native speakers of English understand what you are saying, then you have legitimately conveyed an idea to another person by means of the English language, and therefore have used the English language appropriately.
The word conscience is in regular usage as a verb, along with all of its derived forms, and hence ought to be considered a legitimate word in the modern English language. Consider also the undisputably legitimate form unconscionable. Conscionable means “able to be conscienced.” How can it therefore be legitimate, lest its definition also be legitimate?