You pose a most interesting question, which brings up an issue that occurs more often than most would think. More often than not, prospective buyers do not obtain a title survey before closing (aka transfer of ownership, settlement, transferring the Deed). In today's market, as I cannot speak to when your parents thought they were buying their house, this also happens when buyers and sellers do not utilize the services of a Pennsylvania real estate lawyer to walk them through the risks of the transaction. The consequences, as you will see, can be financially and emotionally devastating.
The risk, which your question illustrates, is that you may not own the property you think you are buying. Assuming the recent survey is correct, in your case, when your parents bought their home, it seems from the facts that you have provided that they really did not own it. You are also correct that the long passage of time that has taken place will play a role here, depending. I say depending because only after 21 years of open, hostile and notorious possession against the real owner's interest (i.e., your neighbor and his predecessors) is it possible to assert a claim of ownership of the property that your parents thought they bought. The legal concept that you are dealing with here is the law of adverse possession and it only kicks in at 21 years of hostile possession. It will depend on the actual facts that have occurred over the years whether you will be able to claim ownership by adverse possession.
I caution you that now that everything is on the table, you possibly have a cloud on title that will prevent you from selling the house. I am not saying that this means that your neighbor is right or that he will win in Court. It simply means that now there is a challenge as to who really owns the property. You will need to quiet title, and that can be done in a few ways. One, by agreement between you and the neighbor, and two, by going to Court to bring a Quiet Title action, and it means just that, it puts the challenges and claims to title to real estate to rest. Your neighbor may decide to bring the action as well, and that does sound like what his intention is (although after he visits a lawyer he may change his mind).
It sounds like you have a good leg to stand on, but you will have to do something affirmative now that you know. There is another possibility but I would not be encouraged. A prospective buyer's title insurance company may be willing to insure the risk, now that so much time has passed. The more likely situation though is that the Title Company would probably want this cleared up before it insures title, which means that you cannot close on the house. You will need to check with the specific title company to know for sure.
I also recommend that you do your own title survey, to confirm your neighbor’s contention. Yes, it is possible, that his survey may not be accurate.
I would not after hearing what I have said here, feel like your neighbor has you over a barrel and that you have to do it his way. He probably wants a concession on price. It is likely from what I know here, that you will be successful in Court, so you have negotiating leverage also. He may be the best one to sell it to, as long as you receive a fair price.
By the way, this issue not only arises with the location of houses, but also with the location of lots of land, driveways, sheds, trees and other shrubbery, walkways, easements, you name it.
If you need to reach me, please contact Gail Marcus, Pennsylvania Real Estate Lawyer, 2 Penn Center Plaza, Philadelphia, Pennsylvania 19102, at 215-751-0505.
Disclaimer -- The information posted is just that, general information and is not to be construed to be formal legal advice or to form a lawyer/client relationship with you. Each case is dependent on specific facts, and one change of fact can change the entire analysis. It is not intended that you rely on the answer that I have provided here, AND NOR SHOULD YOU RELY on what I have said here. YOU NEED TO SEEK LEGAL COUNSEL FOR A FORMAL LEGAL OPINION SPECIFIC TO YOUR FACTS.