It must simply be "notorious" not that you don't have permission. In fact, had the former owner filed a suit at any time ordering the judge from using the land, that would have killed the adverse possession suit. If you have land that is being used as a roadway for someone else, the same rules apply. You are far better off leasing the right of way for $1.00 per year. That changes it from a prescriptive easement to a lease and they cannot come back later and claim ownership or a perpetual right to use it.
You will most often find adverse possession at the rear of lots or side yards of urban lots where the one party has used a foot or two of their neighbors land for a garden or driveway. If the boundaries are unclear and a survey in the future discovers the mistake, if it is past the 18 year usage period, the user can file on and own the property.