Bill your about half right, in order to get legal title to the whole property you have to possess both half's. Actually that's not completely true either if the house sit's on the property line, say one foot over it is probable possible to buy a sliver of the other lot to make this home legal.
The problem is depending on location this may have been grandfathered long ago and the records you found were originals without the statute for use being considered. For example you place a fence three feet over in your neighbors lawn and if never caught that three feet will become part of your property legally over time.
Since you did not say what state? If this home sits equally over two lots they may have been merged under one tax parcel even though the plat records still show two individual lots. This is done sometimes to make one bigger lot to build on, sometimes the lots although owned by the same party are left individually with the intention that the main house is torn down and two siblings then have a lot each to build on.
You have to talk to the city planning and zoning department to see how this house and lots are deemed in the city, county and states eyes!