Let’s turn that around - who do you believe should be paying his fee/salary during this episode to ensure his independence remains (and is seen to remain)?
It doesn't matter who pays, what is more important is who selects the expert.
What follows is a general observation and nothing to do with this specific case. If an independent expert excoriates her client with brutal honestly, then would this affect her chances of future work from other, similar, clients? The way to guard against this potential moral hazard is for such experts to always be appointed by someone other than the client, and who themselves are not paid by the client to make that selection.