I am Spartacus said:
...I am a refusenik re LBS tho'
In that case, you need to be self-sufficient!
It is possible for a wheel to be true and round and still have wildly varying spoke tension. This is not a good state of affairs, because the wheel is unlikely to
stay true for long. Whether all the spokes on a side have fairly equal tension is easily tested by "pinging" them (unless you are tone deaf...). They should be within a semitone of each other.
In your case, if the spokes (on the same side of the wheel) which meet the rim either side of the "dull" one are tighter than most, they could be compensating for the loose spoke between them. If that seems to be the case and tightening that spoke pulls the rim over, try loosening its neighbours.
Alternatively, there may be a spoke or spokes on the other side of the wheel which are less tensioned than their comrades, again (in combination with your notably "dull" spoke) allowing the rim to run centrally - though this would probably be apparent as a roundness blip.
Most of my wheels are tuned in F#