Roger,
You are exactly correct on the physics. The confusion here is one of terminology. You are considering a single motor operated in two difference configurations, Don and I are describing two different motor designs targeted for the same supply conditions.
If I take a particular motor, designed to operate at 240V, which is internally delta connected, and I change the connection to a wye connection, then to operate the machine properly I will need to supply higher voltage, but the machine will draw lower current.
But if I have two _different_ motors, both designed to operate at 240V, one which is internally delta connected, the other internally wye connected, but the motors were otherwise the same (same mechanical output, same efficiency), then the input current will be the same.
Again, please consider the heater example, because this lets us ignore the variability of the mechanical load and ignore questions of efficiency.
Say I want to buy a 30KW 480V three phase heater. The heater arrives as a box with three terminals. I connect the heater to my 480V supply, and 36A/phase flows into the box....For a short time, then the smoke starts pouring out and the ground fault relay trips, since I didn't connect the water
Internally, this heater could be built with 7.7 ohm resistive elements connected wye, or it could be built with 23 ohm resistive elements connected delta. The internal connection simply does not matter as far as the _external_ load is concerned. A resistance measurement between the terminals would give the same 15.3 ohms, either by two of the wye elements in series, or by one of the delta elements in parallel with the other two.
The two heaters would be operationally different if a heating element were to fail, but in the state of normal operation you couldn't tell them apart.
Similarly, I can design a 20HP 480V 2 pole motor, with internal connection that is either star or delta. The _external_ current flow will be essentially the same in either case. If the motor is _internally_ a delta, then the current flowing in a given phase winding will be lower, and the phase voltage higher, but the external voltages and currents, once all three phases were properly combined to the three terminals, would be exactly the same. If I took either of these motors and _reconnected_ them internally, then the _external_ terminal voltages and currents would change exactly as you describe.
-Jon