Passed on by Ken Callicott, presumably from his browsing in supermarkets:
As I note from time to time, N + N compounds (like infant water) are always subject to multiple interpretations, even if we stick to interpretations that involve only the relatively small set of canonical semantic relations between the parts. Usually knowledge about the world and about the context in which a compound is used is sufficient to make one interpretation by far the most likely one. But that doesn’t stop mischievous people from seeking out possible but unlikely interpretations and making antic hay out of them. (And cartoons often show henighted people fixing on possible but unlikely interpretations.)
Ok, for infant water the obvious interpretation is ‘water for infants, to give to infants’ (and the label says “for babies & toddlers”) — parallel to the conventionalized compound infant formula — and fixing on the interpretation ‘water (made) from infants’ is just willful misunderstanding, for the sake of a joke.
But wait! There’s more!
The full label has the larger expression fluoride free [that is, fluoride-free] infant water. The question is then how this is to be parsed — as (p1) or (p2):
(p1) [ flouride-free + infant ] + water ‘water for [or from] flouride-free infants’
(p2) flouride-free + [ infant + water ] ‘infant water [in either sense]’ that is flouride-free’
(where flouride-free is ‘free of flouride, without flouride’)
Of course, if you opted for the ‘water (made) from infants’ interpretation for infant water, you probably went with the even sillier ‘water (made) from flouride-free infants’ interpretation for fluoride-free infant water. Because knee-slapper.
There’s actually a serious real-life point here, which is that babies and toddlers need to be protected from too much fluoride in what they drink. Freedom from fluoride is a plus in water for infants.