This kind of conflict is more sensitive than merely a conflict about LNAB spelling, as it can affect who you and this other member connect to as ancestors farther back. I think that it would be best to delay merging until you (ideally both of you) have pulled together and presented the evidence you have.
I have a hunch that the death certificate may currently be your only source for the name of Downing. (I have this hunch because I have a similar situation with one of my Pennsylvania female ancestors.
) Have you dug into the records for any additional clues that might connect the family to Catherine's birth family? I'm thinking of evidence from wills, census records that name relatives living in the household, land records that may be a family land transfer, and the like.
The other member says that death certificates for several other children of Catherine gave her name as Delameter; that evidence cannot be dismissed easily. It's common for different death certificates to have different names for a parent, so it's a good idea to consider who the informants were and how likely each of them was to have solid information (e.g., was the informant the oldest daughter of the family who likely knew Catherine well, or was it a grandchild or a son-in-law, who may not have had a good recollection of the name?). If several of them said Delameter and just one said Downing, I'd lean toward Delameter unless I knew a good reason to go with Downing.
The other member named a bunch of sources, but citations like "1860 US Federal Census" and "Pennsylvania Probate, Wills and Probate Records, 1683-1993" do not make it real easy to find those sources. It would be helpful if they could show what it is they found in those sources that gives evidence for any conclusion.
The other member mentions DNA, which would not normally be a good clue to confirming a relationship to a 3G grandmother.