In the words of the esteemed sage Jerry Garcia:
Constantly choosing the lesser of two evils is still choosing evil.
I'd advise the individual to get out of the situation as best as he can. There's a similar legend has it regarding Ridbaz, who was a rabbi in Chicago in the early 1900s. He found himself "accidentally" locked into a freezer when inspecting a meat plant on a Friday afternoon. Finally he managed to break out, by then it was Friday night. He got up Saturday morning, said "it's a matter of life and death", and put himself and his kids on the train to New York.
But to answer your question: I'd presume as it's not "big three" (idolatry, murder, severe sexual transgression), he's not obligated to put his life on the line for it. Baltimore's Where What When had a piece c. 2009 from Rabbi Dovid Katz regarding a kosher butcher from long-ago Baltimore; the rabbis had asked that butchers apply tags with the meat's date (so consumers would know that it's been washed within 72 hours); this was the only butcher to do so, and he was threatened with his legs broken or worse; he backed down and removed the tags (though still keeping his meat up to standards).
As everyone else is quoting rabbi stories, here's one: around the year 1770 a man showed up in Prague with some wagonloads of cheese, looking to open a cheese store. He provided the Chief Rabbi of Prague, Ezekiel Landau a.k.a. Noda Bihuda, with a letter from his local rabbi certifying the cheese's kashrut to the highest standards. Rabbi Landau deduced from the way the local rabbi had dated the letter that the cheese was not kosher, but that the cheese merchant could have had the rabbi killed had he not written the letter.
The fly in the ointment is a discussion in the beginning of Ketubot regarding witnesses validating signatures on a document; there is an opinion in the commentaries there that a witness should give up his life rather than sign falsely on something, to preserve the integrity of the system. But I believe we conclude otherwise there.
There is a similar opinion (Maharam Shif I think?) that if someone points a gun at a rabbi's head and says "rule that X is kosher" when it isn't, or "that it's not" when it is, he's obligated to give up his life rather than allowing Torah to be falsified. But it's counterfeit Torah to say "cows are a non-kosher species"; to say "Shmergie's restaurant uses only kosher-certified ingredients" when they don't isn't falsifying Torah per se, it's falsifying reality (which is analogous to the witness case above).
Lastly there's the discussion if Jewish law regards torture as worse than death. The Talmud says that Hananya Mishael and Azarya were thrown into a fiery furnace for refusing to bow to Nebuchadnezar's statue, "but had they been beaten, they would have bowed." Some read that as they would have been allowed to do so. (An alternative reading is even though it's prohibited they would have done so because torture can break Biblical heroes too.)