I am not aware of any such rule as you stated. If a plural object of the preposition follows a singular subject and if a relative pronoun such as 'that' or 'who' is placed after the plural object, then the subject of the following clause is taken to be plural and the verb will be plural.
For that, it is essential to have a pronoun after the plural object of the preposition of the previous clause.
To wit:- see the difference now.
One of the students -- the verb will be -is-.
One of the students who -- the verb will be 'are'.
- Here the verb for the relative clause is plural because who stands for the plural students.
Quote:
The lack of complete historical records from the mid-to-late 1800s have made
This is wrong; there is no intervening relative pronoun after the 1800s. The OA is in line with this theme and confirms the verb is singular.