My hosting provider is being paranoid and refusing to let me post a handful of screencaps from anime series and panels from manga for promotional purposes. (To spice up reviews and so on)

They have already stated that "everyone else does it without problems" isn't good enough.

Does anyone know which part of American copyright law I should quote to prove that they won't get in trouble? I know it's OK for review sites and e-stores to do so without any extra costs.

I am Canadian and so is the parent company but the hosting sub-company is based in Atlanta.