Do Americans overseas have any right to complain?

It does from the standpoint of desire vs need. If the entire country is not under attack than there is more desire than need to evacuate. The speed of evacuation is a function of cost and should reflect the nature of the situation.

My WAG is that there was a need to vet the people wishing to be evacuated due to the nationalities involved. Many of the evacuees had dual citizenship and were living in Lebanon (as opposed to visiting). I suspect there was a desire to filter out potential terrorists. Lebanon is a country that allows political parties to maintain a private army (Hezbollah) that is financed and armed by unfriendly outside interests.