Too dead to test is a helpful, if shocking phrase.
In order to complete brain stem tests, for example when organ donation is being considered, the patient's vital signs have to be within normal ranges.
As an example, when people are very cold their metabolism slows and their oxygen requirements fall. There have been cases of people who were very cold, often after being in water for a long time, being successfully resuscitated.
For this reason, you can't conduct brain stem tests if someone is too cold. They wouldn't be valid.
I haven't read the court documents, but assume that Archie's condition is such that it would not be possible to conduct valid tests and so the legal standard for BS death cannot be met.