He'd have made life easier for himself and the family by saying "this won't work, but if you can foot the bill and will feel better about it then OK".
Ivermectin is prescribed (not proscribed) mostly for treating parasitic infection. Using it at therapeutic doses for Covid is dangerous.
But I'm not forcing my standards on anyone. If this family wants a silly treatment and there isn't anything better to do, then they should get what they want if they are willing to pay.
One of the reasons this doctor got screamed at is because he took responsibility for making all the decisions and the patient died anyway. Which is good doctoring, I respect that. But if he is surprised that a family is angry that he ignored their wishes without a good reason then he is not paying attention to how the world works. He could have easily just agreed with them and kept the peace, at no undue cost to anyone.
Are you a doctor, healthcare provider, or even in the medical field? If not, I urge you to stop spouting your amateur theories about medicine on the internet, where they can spread and cause further harm.
This isn't a conflict situation and there is no obvious downside for anyone. The doctor isn't giving in to anything. The family is making a stupid request, yes. No skin off the doctors nose to grant it though and if it'll make them happier he may as well. If he thinks it is significantly harmful then he needs to make that argument instead of dismissing them.