Sometimes even a survey isn't conclusive. Most of you have probably heard that there's no money to be made if you're the only lawyer in town. Sometimes surveys don't agree, just like lawyers. I've had several real-world examples.
Case 1: Some years ago I was hired to design an energy-efficient house for a single guy, on an existing lot in a rural community. First hint that this wasn't a good plan was that the street had been subdivided ten or fifteen years prior and this was the only lot that hadn't sold, but ... my client had already bought the lot, so we proceeded from there. Skipping over several other issues, we had the subdivision map -- which was a legal survey, signed and sealed by a licensed land surveyor. I went out with the client to walk the site and try to figure out where we wanted to situate the house. Conveniently, at the right side of the parcel (viewed from the street) the property line coincided with a telephone pole, so it was easy to orient ourselves.
And as I stood at the telephone pole, something didn't look right. The adjoining house looked MUCH too close to the property line. I recommended to my client that he have a new survey made. He did. Turns out, the neighboring house was in violation of the zoning ordinances for that town. The side yard setback was supposed to be a minimum of (IIRC) 25 feet. The house was actually about five feet from the line. Apparently, whoever had laid out the foundation used a compass, and either forget or didn't know to correct from magnetic north to true north. Not only was the adjacent house much too close to (but not over) the property line, their undergound electric and telephone trench was ON my client's property. At that point, my client's attorney told my client that I had done him a favor, and the lawyer recommended that the guy sell the lot and walk away. He did -- he bought an old colonial house near the center of town.
Case 2: I was, for awhile, chair of my home town's planning and zoning commission. We had an application before us to subdivide a large-ish parcel into several building lots. All subdivisions in this town are subject to public hearing. When the hearing was opened up to public comment, a woman stood up and said that part of the land shown in the subdivision was actually hers, and she had a survey to prove it. Sure enough. The application had a survey, by a licensed land surveyor, and this woman had a survey, by a different licensed land surveyor, and they didn't show the same thing. We had to tell her (unfortunately for her) that we couldn't help her. Our job was to determine whether or not an application complies with the zoning regulations. We were not a court with any authority to adjudicate disputes over ownership of property.
Don't know how that one ever played out.