As it happens, it was -- the form was subtly broken. I eventually managed to track that down, but it leaves a very different question mystifying me: why the heck does $query->Dump() manage to show the fields parsed out perfectly fine (including the broken ones), while the individual $query->param() calls fail to do so? There's something very weird going on in that library -- either the internal data structures aren't consistent, or there's a subtlety I'm missing...
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