Hi.
It seems not, from the datasheet:
"The LT6220/LT6221/LT6222 have an input and output signal range that covers from the negative power supply to the positive power supply."
But I agree with you, paragraph 3 page 1 says what looks like the confusing opposite, which note 2 seems to back up or not to a degree: "Note 2: The inputs are protected by back-to-back diodes. If the differential input voltage exceeds 1.4V, the input current should be limited to less than 10mA." Maybe meaning 12.6V + 1.4V...
I just understand that bearing in mind the total supply voltage (12.6V), the input - and + signals need to be within a 12V framework, like -5 to +5V, or 0V to +12V, but not -5 to +9V, for example.