Maybe the neutral "gave". A floating neutral could get you close to those values if it floated outside the delta (like ~ high-leg to neutral = 237v, other legs to neutral = 123.5v, phase voltages = 240v).
A very interesting hypothesis! It definitely could let you measure that combination of voltages, which are close enough to what the OP described to be attributable to a low accuracy meter. There is no combination of loads from the three phase wires that could cause the neutral to move outside the delta like that and stay stable, except if there is higher voltage wye or delta involved in the situation too. Could be though....
One thing that could move things in that direction would be a 180 degree phase shifted version of the OP's A leg (or B leg if you correct the naming) voltage.
Or, if you actually had a wye secondary, fed the three phase wires from the points and then ignored the true neutral of the wye and instead drove the neutral wire through a transformer whose primary went from A to the wye center point and whose secondary went from the wye center point to the "neutral" with reversed polarity and tapped short of a 1:1 ratio it might actually look very close to what the OP reported. You would not need to have a center point on the low phase secondary to derive that either. The "120" voltages would definitely be high though.
Hmmmm?! Nahhh. (?)
The new fourth wire voltage would be located (on a vector diagram) on the arc of a circle whose center was on the high leg and whose length was 240.
Maybe....
