I guess a can is better than cheap plastic that leeches into the water?
I suspect this case, after reading about it in between actually working, that the claim is actually more scoped than I'd understood, because it is primarily about the recyclability of the can and not a literal claim of zero plastic.
That is, in fact, on me, but given that this isn't an aspect of the product I care about, not entirely shocking to me that I misunderstood. And I got to learn a fun fact about aluminum cans that I didn't know before!
Canned water is a plastic membrane holding water with aluminum on the outside for structural integrity.
Same with boxed water but cardboard replaces the aluminum.