Yeah, but copyright is not a form of traditional property right. Intellectual "property" rights are better thought of as intellectual monopolies granted for a limited time, and this is important because intellectual works have some very different properties that separate them from physical property.
For instance, in your examples, the lawn mower cannot easily "un-mow" the lawn nor the painters "un-paint" the house. Any attempt to do so would be labor intensive. However, in the OLGA copyright case, the publishers can trivially force the infringers to no longer publish the tabs, undoing any further damage. In the lawn mower and house painting case, the labor is fundamentally tied to the physical property being infringed. However, with intellectual property, this is explicitly not the case. The tabs do not alter the original song in any way, they are merely a derivative work.
To be explicit, while the transferal of rights over the tabs to the copyright holders may be granted by a judge as part of reparation of harm done, I see no reason that the music publishers should presume to own the rights outright without the intervention of a court.
For one final example as to why we should not conflate intellectual works and physical property, if I were to trespass onto your land and paint a beautiful painting of your landscape (with supplies I own) and then leave without causing damage, do you... own the painting? Just own the copyright? Own none of it? It is definitely not clear to me that you should automatically own my painting, even if I infringed your property rights by trespassing.