Typically sod is fertilized just prior to cutting and shipping it. The grass should be good for the winter.

What the lawn care company said seems correct, but I believe they missed the window for "fall." That might have worked in September. It sounds like they are using organic fertilizer. Organic fertilizer would never damage grass or the soil unless you smothered the yard with it. So I believe it is not really needed but it won't hurt anything if they use it. Another consideration is that the soil temps are getting too low for organic fertilizer to do anything now. That gets back to my comment about doing this in September. I would do nothing now and continue doing nothing until next May. Then use an organic fertilizer. All the fertilizer companies start advertising in about February to apply NOW. Resist the urge. Magical biological things happen in the winter, so the grass should not need anything until May. Even if you apply early, it will still need to be fertilized in May, so save the money and wait for May. Check for weeds in mid April and spot spray with Weed-b-Gon as needed.