I think the recollection here is about the writ of quo warranto, a legal procedure for establishing somebody's claim to have a certain legal right. For its purposes, the cutoff point was 1189. It is not necessarily about the owning of land, but about feudal privileges possessed by people other than the king. Examples of "franchises" or "liberties" included hunting rights, the ability to hold courts and receive fines, levy tolls, and so on. They would have been granted by royal authority, in theory.
Part of Edward I's programme was to claw back those privileges, motivated by some combination of wanting more revenue, more power for himself, less power for barons, more opportunity to hand out patronage again in a different way, to display justice being done, to simplify an uncertain legal rule, and to establish exactly which privileges were valid. So he took the opportunity to beef up the legal means for challenging the franchises, over a period of several years with a few different systems. Historians differ about whether they conceive this process as part of a master plan of domination over the country, or just an administrative change.
The eventual rule as of 1290 was that a subject could challenge the purported exercise of a franchise, by a writ of quo warranto before a justice-in-eyre. (That is, one of the circuit judges who roamed around the country, as opposed to the more difficult process of appealing to the King.) A statute of that year said -
qui per bonam inquisitionem patrie aut alio modo sufficienti verificare poterint quod ipsi & eorum antecessores vel predecessores usi fuerint libertatibus quibuscumque [...] ante tempus Regis Ricardi consanguinei sui aut toto tempore suo & hucusque sine interruptione continuarunt & ita quod libertatibus illis non sint abusi [...] dominus Rex statum eorum affirmabit per literas suas.
Who by good inquest of the country, or by other sufficient means, can verify that they and their ancestors or predecessors have used any manner of liberty [...] since before the reign of King Richard our cousin, or in all his reign, and have continued without interruption, and that those liberties have not been abused [...] then our lord the King shall confirm their estate by his letters.
Prior rules were not clearly established for how long the liberty would have to have been enjoyed. For the year 1189, there is nothing too magical about the number. It is about a century before 1290. Defining the time with reference to regnal years is convenient for a legal context when documents would have been dated using those years - or at the very least, identifying the name of the King who granted the franchise, and thus whether the event was pre- or post-Richard.