There seems a lot you haven't found. Did you not notice the part that explicitly states only OAT not TAT (or SAT) is to be used for determining icing conditions on the ground. Its in the FCOM and AFM which forms part of the certification of the aeroplane.
Does the FCOM or AFM allow use of the EICAS Engine Anti Ice On message to turn the protections off on the ground ? Absolutely not , it states:Use the temperature and
visible moisture criteria because late activation of
engine anti-ice may allow excessive ingestion of ice
and result in engine damage or failure.
Guess where the EICAS Engine Anti Ice On message comes from ? The TAT probe (or SAT probe if you want to call it that).
There are actually 3 TAT probes on the 777 that are used for engine take off thrust calculations but that process is complicated and certainly not part of crew icing diagnosis.
Are you aware of all the regulations on how airfield temperature has to be scientifically produced to be officially reported ? Perhaps a visit back to the books to look at Stevenson Screens and some ATPL bits is needed.