Whether something is “correct” or not in this particular grammatical regard comes down to cultural factors, not objective linguistic ones. If we look at the languages of the world, we can see plenty of cases where the nominative form of the 1st person singular pronoun was gradually replaced over time by the accusative or oblique form. Therefore, people coming to say “Tim and me” instead of “Tim and I” is a completely natural linguistic change and complaining about it is simply being pedantic.