[happytoexplain]

There is no contradiction between accurately repeating and paraphrasing. You can do either or both or neither. Yes, paraphrasing is dangerous in your context (repeating to a 3rd party), but it's fantastic in the quoted context (confirming understanding with the 1st party, which can not happen if you repeat using the exact same words).

[ipadmini]

Agree. Paraphrasing and mirroring are two different ways of reflecting what the speaker is saying. Some situations call for both. In imago therapy (meant for couples), the script calls first for mirroring (repeating word for word), followed by a summary (to demonstrate understanding, and to seek clarification).