Reversed and Forward Biased Diodes in Parallel
Your intuition is correct, however you assumed that the voltage drop on the current source I1 is zero, which is incorrect. It is like to assume that a current flowing through voltage souce is zero. On the contrary - you can imagine that a current source generates whatever voltage is needed in order to cause the current to reach the specified value.
Lets consider resistor R1. Its left side is being held on voltage 1V by V1. Its right side has the voltage V, which we are looking for. The current through R1 is IR1=(1-V)/100R, flowing right.
Similarly, the current through R2 is IR2=(V-(-1V))/100R, also flowing right.
The current through both diodes D2 and D3 is I1=1A, it does not matter which diode is conducting.
Sum of the currents in point V is zero: -IR1+I1+IR2=0. Therefore:
-(1-V)/100+1+(V+1)/100=0
(V-1)+100+(V+1)=0
2V+100=0
V=-50V