"この町に住ませて頂きたいんです。" is a line from a movie. That grammar makes sense to me. In this context, 使役形 is used to create a humble mood. (頂く) makes it even more humble.
Based on that, today I said: "３年ぐらい、広島に住ませて頂きました。" I was told that is incorrect. In fact, this is correct: "3年ぐらい、広島に住ませてくれました。" This grammar confuses me.
I feel that "この町に住ませて頂きたいんです。" should be sounded-out into passive voice: "I want to be forced to live in this town."
However, I don't know how to sound-out "3年ぐらい、広島に住ませてくれました。" into passive voice? By using 使役形 in this context, I am just pretending that someone has power over me (so as to humble myself). But, when I hear 「くれる」, I sense that the two parties must be specified (me and someone else). But, since I am just pretending there is someone with that power, there really is no one else.