Martin (1992: 224):
There are even fewer distinctive internal temporal conjunctions than consequentials, and so the discussion here will be very brief. Simultaneous text time is realised through at the same time which connects messages that are rhetorically overlapping:
[4:150] One of the main questions we must again ask concerns the balance between the social and the individual. For language, in the sense of knowledge of the linguistic items and their meanings, the balance is in favour of the social, since people learn their language by listening to others.
At the same time, each individual's language is unique, since no two people have the same experience of language.
This use of at the same time is neither internal nor temporal. Despite the inclusion of the word time, no temporal relation is being construed here — internal to the unfolding of discourse or otherwise.
Instead, at the same time marks a concessive conditional relation, like the similar conjunctive Adjunct all the same. (See Halliday & Matthiessen 2004: 543.)
It is perhaps a little ironic that, with the category concessive having been misapplied so many times up to this point, a genuine instance is not recognised as such.