Not really. I wouldn't debate they experience it at any level of society, but there are lots of completely different social systems that each race can exist in. There's not much commonality at all in the kinds of experiences a black person growing up poor in Alabama and a black person growing up middle class in a Haitian community in New York will have. It's the same way the WASP-y family my dad grew up in is in a different world from the Italian Catholic neighborhood my mother grew up in. They're nothing alike.
Do they have to have the same kind of social experience as the predominant history they're teaching? Well, that'll be tough, given that the kinds of minority people who come out of college are inherently better off than the most subjugated of their people, not to mention they weren't even alive for most of it and thus have no experience with it at all.
But even if we just accept that on its face, then, again, what you're saying is that not only has no white person ever experienced social injustice, but they are simply intellectually incapable of understanding it. And if you think that, then perhaps you need to watch some
Tim Wise. Heard about him through a black professor, by the way, who (rightfully) made no claims that her Ivy-league educated self had any damn idea what it was like to be a black person at the bottom. Because her social experience was different. Her blackness didn't imbue her with psychic knowledge of every type of black culture in the country.