Gluten free sodas are gluten free to a point

So I'm enjoying a lovely beverage at Hunters & Gatherers [1] when I notice something odd on the label:

[I don't care about the wheat content as much as I care about the corn content.] [2]

“Pardon my asking,” I said to the proprietor, “but I thought all soda was gluten free.”

“I would think so too,” said the proprietor. “Perhaps for sweetening? Like stevia?”

“No,” I said. “It's usually corn they use for sweetening.”

“Oh,” said the proprietor, who was doing a search on the Intarwebs [3], “sodas might be bottled in a shared facility.”

“Okay, that makes sense.”

“And if gluten is less than 20 parts-per-million, it's considered ‘gluten-free.’”

“How about that?”

“Well, the more you know [4] …