To add a bit from an ATPL theory perspective, which part of the interviewer's distant past may be where this question originated, the balanced field length calculation starts by assuming ASDA=TODA and then produces a solution for V1 and OEI FLL TOM where ASDR=TODR. Possibly relevant is that the EASA definition of balanced field in the theory exams is that ASDA=TODA. I'm struggling slightly with JT's statement that additional stopway or clearway leading to an unbalanced solution may produce a greater OEI FLL MTOM, by my understanding it will always produce a greater OEI mass. Could you expand, please JT?
Concerning the original question it only needs slight rewording to make it 'Does the field length for take-off always have to be balanced?', which improves it no end and can lead to an interesting discussion about where V1 goes and where the FLL TOM goes with, for instance, increased stopway. These questions feature in the ATPL exams, Maybe it was one of those.