I have hired heaps of times - usually through Avis but sometimes Thrifty.
I usually call themand tell them the age of child and what configuration i want - including spacing of the straps and then i check it when i pick up the car. they are very happy to tighten it up etc i have found. i have never had any probs and have done rear facing and front facing. i also tell them where in the car i want it (ie benhind passenger or whatever)