Leader in assault without troops

[J6A]

I had a situation arise in a scenario today. The Germans had an armored car, and 8-1-0 LT, a GREN and an HMG in a hex. US OBA demoralized the GREN and HMG who promptly fled. The leader chose not to go with them and to stay with the Armored Car.

The US then assaulted. Do the Germans get the modifier for the undemoralized leader in an assault hex in this situation? I assumed that they did. It doesn't say "with other units." I did not give them the 1 FP for the leader (as that will only adjust other units), and wasn't 100% sure about the shift.