The Court of the Lord Lyon, the official authority on these things, states on the matter (bolding mine):
> A dwelling house of whatever size presents no problem, but the ownership of forestry land or “amenity” land on which there is no house and for which planning permission for a house would not be obtainable would not necessarily be sufficient to bring the owner into the Lord Lyon’s jurisdiction. _**The ownership of “souvenir” plots of land of a few square feet or thereby such as are marketed from time to time, is insufficient to bring anyone within the jurisdiction of the Lord Lyon King of Arms.**_
So, just getting a coat of arms, let alone the title of Laird, requires ownership of a substantial amount of land. Therefore, the claim is false.