The difficulty with that theory is that it's not supported by the Bible and actually contradicts and runs counter to the Bible that YECs say they believe in and take literally. For example, Genesis 2:14 directly identifies the Tigris River as the river which 'flows east of Assyria', the same river we know today as the Tigris River and the identification with Assyria shows the river still existed (on the surface of the earth) during the time of the patriarchs (instead of being buried five miles underground below the Paleozoic). Same thing with the Euphrates River, which is mentioned in Genesis 2 but also again in Genesis 15:18 with the Abrahamic covenant when Yahweh tells Abraham the land of his descendants will extend from Egypt to the great river Euphrates that is still so-named today. Thus, given Mosaic authorship of Genesis, Moses understood the Tigris and Euphrates Rivers associated with the garden of Eden as the same Tigris and Euphrates known in his time and known to us today.
This stands in direct contradiction to YEC flood geologists who insist that most of the fossil record was put down in Noah's flood. It is also difficult to reconcile with those who insist there was no death of any kind before 'the fall', since that too would require the garden of Eden to predate all the death in the fossil record.
Just a somewhat unrelated point, we have no idea where the Garden of Eden was. just because the named rivers in Genesis match rivers around today doesnt mean they are the same rivers. New York, New Mexico, New Jersey.... people like to name things after things from the old land. The rivers mentioned may have been completely different, pre-flood rivers.