Why is kosher wine or grape juice rare alone but less so as an ingredient?

My understanding is that wine or grape juice is s'tam yenam and forbidden if handled by non-Jews without having been cooked. (See, e.g., an explanation on chabad.org.) The practical result of this, for the consumer, is that wine and grape juice (in the United States, say) are almost always manufactured by a religious-Jewish-owned company, or on a run for its label: one hardly sees wine or grape juice on the market that is kosher but manufactured by a general-market company. Yet one does see general-market, kosher goods with wine or grape juice as an ingredient. Why?

• Is it that some heter, not relied on for pure wine or grape juice, is relied on when the wine or grape juice is merely an ingredient? What heter?


• Or is it that I'm wrong that s'tam yenam is the reason that major brands' wine and grape juice isn't kosher, and there's some other, not halacha-related reason (which therefore doesn't apply to such wine- and grape-juice-containing products)? What reason?


• Or what?

As an example, Kikkoman Foods's Teriyaki Marinade and Sauce lists wine as its second ingredient (right after soy sauce) and is certified as kosher by the Orthodox Union (as of this writing). As another, many a brand of dijon mustard, containing white wine as an ingredient, is certified kosher by, for example, OK Kosher.