You are correct. In a sense, the pronoun is acting in a double way: as an object in the parent clause and as a subject in the dependent clause.
The received rules of English say that the correct choice between "whoever" and "whomever" is determined by whether it is used as a subject or an object in the dependent clause. When, as in your example, the pronoun is the subject of the dependent clause, the correct choice is "whoever."
"Whoever" and "whomever" lead to a more concise and vigorous style. "The words en huios alert any person who reads the epistle" shortens to "The words en huios alert whoever reads the epistle." And obviously "The words "en huios* alert any person whom reads the epistle" is grossly ungrammatical. You will not make a mistake if you recognize that "whoever" is a contraction of "any person who" and that "whomever" is a contraction of "any person whom."
The pretentious who have not been taught the received rules think that indiscriminate use of "whomever" shows a high style. What it actually shows is ignorance or carelessness. Because Greek is an inflected language, I'd place no confidence in a writer who does not understand inflection in even the writer's native language.