"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.
この町に住ませて頂きたいんです
is more like "I want to be allowed to live in this town". But your phrase usingいただきました
sounds fine to me. Did they say why it was incorrect?