I don't know where this is documented (I'm sure it must be somewhere), but having played with it a bit, it seems that perl's "UTF-16" (no "BE" or "LE") means "There needs to be a BOM at the start".

Perl will write a BOM on initial output to a file handle that is set for this encoding (and will use your machine's native byte order). On initial input, it will error out with "UTF-16:Unrecognized BOM xxxx" unless the first two bytes are either 0xFF 0xFE or 0xFE 0xFF. (And yes, if the first two bytes are one of those two pairings, it will use the given byte order.)