OHM'S LAW?

 
V = R.I               →  voltage directly proportional to current
I = (1/R).V          →  current is directly proportional to voltage

but the proportionality factor is obviously not the same one.

Both. Voltage directly proportional to current & current is directly proportional to voltage. The two statements mean the same.

If R is a constant, then V is directly proportional to I and I is directly proportional to V. The two statements are equivalent and follow from each other. Each one is a constant times the other.

If R is not constant, that is if you are comparing situations with different values of R, you can't say this.

V is proportional to I, This gives V= K I, K is called resistance.
I is proportional to V. This gives I = M V. M is called as the conductance.
If you take care of constants K and M then both are equivalent.