It may be the case she was given those parents as a hint on one of the big genealogy sites, and with no other possibility showing she believes it to be fact.
If there is no reason to believe Patrick and Mary moved their family to Cavan when they were still quite young than there is no reason to believe your Rose would have claimed to be from Cavan.
It's also not impossible that there is more than one couple called Patrick Cullen and Mary Quinn having children around the same time but unless she has at least the marriage of Rose and Terence than she can't even prove Cavan Rose's father was called Patrick.
You need the marriage cert to get to the birth, one step at a time, leave out a step and even if you have the correct record you can't prove it.
It's a shame a marriage for Dublin Rose hasn't been found but she may not have married or may have died young.
