For the V1 case, it's also due to the lower (sometimes signifcantly) thrust output of the remaining engine.
You say you are using balanced field numbers. (As most carriers do.) Then, unless you are at Max T/O weight, you are not runway limited. You will (in most cases) see a slight increase in indicated V1 due to the unequal effect of DA on thrust vs. brakes.
For a very simple example, let's say the increase in DA (at the same weight) will cause an increase in takeoff distance of 200 feet due to the above mentioned lower trhust. But...the increase in stopping distance (due to the higher TAS) is only 100 feet. The V1 speed will be increased by a knot or two to once again balance the takeoff.
In a nutshell, at a higher density altitude, the degraded thrust on the remaining engine is more of a factor than braking from the higher TAS.
