pylon:
The chip operates only at 3V3 (according to the datasheet, page 2: absolute maximum ratings for Vcc is 4.0V), so maybe that information is just wrong and you have to drive it with not more than 3.3V to get reliable results. It's possible that the module includes a voltage regulator but we don't know it. You might measure the voltage between pin 1 and 4 of the chip during operation.
When operating the voltage between pin 1 and 4 of the MAX31855T on the breakout board is 3.109 V, which I think is just within the recommended operating range of the chip as per spec sheet (3.0v to 3.6v). Im feeding the breakout board with 5.06v from Vcc on the Arduino so I guess there must be a voltage regulator on the board.