I am not sure that's true and here's why: If I book a BA flight on Expedia I can use BA's online check-in and sit anywhere on the plane I want, if no-one's got there first obv. There's no bit of the plane that's "Expedia class" all together.

I suppose any travel agent could do that on-spec, but in normal operation travel websites are just brokers sitting on top of the same API the airlines use for their own sites.