I'd guess it's more like "four adventurers hunting for easy magical monster stones, (at least) one of them an archer who took a shot at the bird". If the bird had been the main target they'd probably have searched longer, now it seemed mostly like "ok, can't find the bird or the arrow, welp, can't be helped I guess, now let's go looking for some weasels or maybe a deer or something, we gotta be done before nightfall".
Reminds me of a casual conversation my sister once had with a predominantly French-speaking man, who was aghast to accidentally learn that Captain Jack Sparrow was named after, not some majestic bird of prey (they were aware "sparrow" was some sort of bird), but the moineau (as he knew it), the teeny-tiny seed-feeders.