Are you sure you are not in mexico?
Sounds like a delta corner grounded service. The smaller conductor is sized according to the loads imposed on the entire 3 phases. Your description suggests that one of the phases is grounded, producing the corner-grounded voltages you are getting.
The "B" phase may be the center tap of one of the windings, which usually is grounded in delta connected configurations.
Your description of "center-tap grounded open delta" might be better stated "center-tap grounded corner delta"
What are your voltage readings from:
A to B? (I'm guessing 120?)
A to C? (you stated 240)
B to C? (208 perhaps?)
A to ground? (You stated 240)
B to ground? (You stated 120)
C to ground? (You stated 240)