sorry but for the unidirectional one of the top post, the "0.1 x vcc" that gets outputted for zero current is just due to the output opamp not being able to take its output down to 0v........the "0.1 x vcc" is not stated as being an offset, so for a sensed current of 1.5A, the output would be just 0.6V, surely?
In the bidirectional case, with a single supply, the output does need to have the permanent 2.5V offset so that you can distinguish between current flowing in either direction, so that is surely a different case.
The datasheet on page 8 states that the actual offset voltage is only 15mV. -Noting that it is not calling the "0,.1 x vcc" an 'offset'...because it does not come into play when the sensed current is above 1.25A, surely?