In relation to objectivity, I thought that the Catholic Church argues that in transubstantiation, the bread and wine actually become the flesh and blood of Christ. OK, they don't say 'objectively', but that is the same meaning. In other words, it's not symbolic or a simile or a memorial or anything like that, which some Protestants say. I guess that AB accepts this. Of course, there is no evidence for this, but you do get some hoo-ha about substance and accident, derived from Aristotle, and therefore true!
Council of Trent (1551): "that wonderful and singular conversion of the whole substance of the bread into the Body, and of the whole substance of the wine into the Blood – the species only of the bread and wine remaining – which conversion indeed the Catholic Church most aptly calls Transubstantiation".
I assume the same is true of things like resurrection - for Catholics, these are not symbolic things, but actual historical events, recorded by eye-witnesses. Hence, this is about objectivity, isn't it, or certainly, factuality.