Not sure that would embaress the refs. I'd think we'd be surprised by how little a third party would change the eventual results.I've often thought on reviews they should be handled by a third party, and they shouldn't be told what the call in the field was. If it's 51% one way then that's what the call should be regardless of what the on field officials said. But they'll never do that because they don't want to embarrass the refs even if it leads to more calls being made correctly.
The calls that would embarrass refs are the subjective ones and the ones that can't be challenged.