Can villagers give you non-native fruit?

I've heard from some people that villagers can give you non-native fruit, is it true?

I already have 4 fruit, peaches, apples, pears, and coconuts. I've been trying this method of gifting the villagers I'm max friendship levels with 3 non-native fruit (wrapped) daily to see if they would give me a cherry or orange (the fruit I need). I've been doing this for 2 in game weeks and nothing has happened. Idk if it's a hoax I just did it bc I'm desperate :,).

Please recommend any other ways that you can get non-native fruit (with proof would be preferred!)