From: Rabbi Akiva Eiger
To: Rabbi Yaakov
Rabbi Akiva Eiger proposes a middle-ground distinction to reconcile the Shach and Urim VeTumim: when witnesses have no independent knowledge of the item's ownership, the principle of hapeh she'asar applies and a simultaneous purchase claim is not an admission; but when witnesses independently recognize the item as another's, the possessor's claim is irrelevant. He applies this framework to related disputes in Simanim 133 and 146 and to the Rosh's position on pledged documents.
Source: Shu"t Rabbi Akiva Eiger §135