Pronoun case in this sentence

"It is very seldom that mere ordinary people like John and me/I secure ancestral halls for the summer."


I immediately thought it was 'me' because 'like', in this sentence, is a preposition, so it should be in the objective case. However, someone argued saying this:

People is the subject of your sentence, and the people indicated are also the subjects (renamed). Any such person refered to by using a pronoun should be presented in the nomnitave case. For the 1st person singular, that person would be "I".

I see where he is coming from, but I do not believe he is correct. It is not an appositive; that is, the subject is not being renamed; 'like John and I/me' is examples of the subject but not the whole subject.

I'm almost certain I'm correct, but I wanted a second opinion first.