In the past, I've read objections to automated theorem provers from the opposite perspective. I kept waiting for that article to bring it up, but they never did. You never know if there's a bug in the code that might lead to a bad proof, so you can't consider something to be proved unless it has been through human peer review.

For things with large real world costs and consequences, I think it's a good idea to have both human and automated inspection, but that's more of an engineering thing than number theory. There's a cost involved in translating from mathematical notation to a language that the theorem prover understands, so you have to choose the places where you're going to go through all that effort.