When we decode whale clicks, are we finding their meaning or our own?

Read about the sperm whale 'phonetic alphabet' work and it's been scratching at me all evening. Spent decades in booths chasing the right word, and now they're finding combinatorial structure in codas — which is remarkable. But knowing the structure of a signal isn't the same as knowing what it means, is it? For those who've worked across languages or studied animal communication — where do you draw the line between understanding and simply recognizing our own shape in the noise?