I've seen and used quotations that I'm not sure is correct. If it is correct, I'd like to know what it is called. If it is incorrect, I'd like to know how to punctuate it correctly. Here is an example of this usage in a hypothetical text conversation.
Mary: I cleaned him out.
Joe: Wait, do you mean, "I won all of his money, so now he has none"?
To add some clarity, I believe the second example below also illustrates the same usage of quotes.
Bob: I think I heard him say, "I like you".
Bob hearing "I like you" is purely hypothetical. It's possible that Bob misheard "I despise you" for "I like you".
Is it correct to use the hypothetical content within quotes? If not, how should it be punctuated?
Every definition of quotation or quote, and every rule I've read regarding their usage mentions an origin or source of text or speech. To me, this implies that there must be an original source in order for something to be considered a quote. However, in the cases above there is no original source as the whole quotation¹ is made up.
Is there an authoritative definition of quotation that includes a hypothetical or entirely paraphrased quote¹? Or if no such definition can be found, is there an example of this type of quote¹ in an authoritative work?
¹The usage of quote or quotation here may be incorrect in accordance with the outcome of this question.