What’s the deal with OU-D soy milk?

I’ve noticed that many brands of soy milk have ou-d on their refrigerated products, but not on the tetra packs. They’re not manufactured on equipment shared with dairy, so what’s the deal? What would be the issue using it in meat keilim (with otherwise parve foods)?

I’m ideally looking for information over speculation – ie, ‘oh this brand uses tanks they bought from a dairy farm, but that’s not required on the allergen statement’ or ‘the ou policy is x’. My dairy allergy is highly sensitive to cross-contamination, so I know that’s not the reason.

I just learned Costco discontinued their soy milk, and the replacement product won’t come until spring (and those in test markets say it’s not as good). I have a severe dairy allergy, so my kitchen is meat-only, and I really need an affordable replacement.

I know someone associated with OU Kashrut is active here, so I’m really hoping you see it.