Applications for Grave Reopen always have the burial date AFTER the listed Record day. Here is one example. The second page looks like it shouldn't be indexed.
I think we are supposed to type what we see. In this case the record date is 15 Sep 2010. That is what the indexer put in. I would agree with the indexer in this case. I do agree with your correction to the name.
They do need permission to reopen the grave before they can have the next burial.