Hmm... problem went away randomly. The post is too old to change the title to "...seemed broken for a minute there", so sorry for crying wolf.
But it got me thinking. The square wave made me wonder if there was some form of anti-denormal square-wave injection at work (maybe it was being inserted into the MSB rather than the LSB of the 64-bit signal)?
It would be good to know if this technique is indeed used - if so, the bitwise operators wouldn't be 100% exact.
While I'm on the subject, does anyone know if there is a tiny error margin for equality in the MSP comparison operators, or are they bit-for-bit exact?