No, it is not connected in any way with the definition you quote. It just means TODA=ASDA.
'Balanced Field' graphs were used by the RAF V bombers. They didn't have regulated take-off graphs for all the runways they used so they carried graphs for 'standard' airfields of, for instance 9,000ft TODA and 9,000ft ASDA at sea level, 1000ft and 2000ft reasoning that, if they found themselves at a SL airfield that had a TODA of 9200ft and an ASDA of 9300ft and they could get airborne using the 'balanced field' 9000ft graph they were erring on the side of caution.
What European CAA policy are you referring to?