Pearl Dreams,
You're right. Those claims are farfetched and their akoya pearls are indeed treated in some way or another. All akoya pearls are, and to claim otherwise means they are either intentionally misleading or not full educated about what they're selling - I would assume the latter based on the strange misinformation in their education sections. They've either been told a few stories or they've created them.
You're also right about Tahitian pearls. I guess it is possible to dye them darker, but I've never seen it before and know of no processors that do it, and to warn about it as though consumers need to watch out for it or to imply that only they don't is really strange. When Tahitians are dyed, they are dyed chocolate or pistachio.