I would tend to disagree with the quote from stoicfury's answer to the other question -- though not necessarily with the claim as it relates to us.
(1) It is possible to articulate non-trumpable types of claims -- the key is just to articulate them in a way that includes that. This may seem merely semantic but it is meaningful. So for instance, if I define the first cause as the cause that precedes all other events of cause, then that definition is not trumpable. It requires us either to deny the standard account of causation or accept there is a first cause. (Generally, those who don't want a first cause assume the former route). What it doesn't do is allow there to be a pre-first cause, because the first cause is definitionally which ever one came first. In this respect, first cause is more a concept than a term that by definition points at something specific.
(2) Since it doesn't automatically point at something specific, it doesn't resolve certain questions. Thus, it doesn't mean we can know the specific content of these sort of ultimate terms. At this point, there is room for false identification between something we like and an ultimate purpose. This sort of point is well-considered in Anselm's ontological argument and the debates after that. The trick to Anselm's argument involves compounding multiple features of perfection together.
(3) Moreover, a term like "ultimate purpose" is harder than "first cause". Because to get to ultimate purpose, we have to have an account of purpose where it makes sense metaphysically to say there is an ultimate one (e.g. Aristotle's teleology). That being said, I don't think it's automatically a fallacy to assert a first cause or ultimate purpose, and they are not subject to trumping if they are definitionally sound. But what can be subject to error is our identification of a specific thing with an ultimate term -- because that identification can err.
(4) You can also choose to deny the existence of any such objects, but then this is not to say that people are using the terms fallaciously -- just that there's something else that makes the terms wrong, i.e. an error in metaphysics or in understanding purpose or cause or motion.