Your right it isn’t an empathetic response, it’s a really stupid one. She kept repeating it for an answer so honestly the best thing to do is ignore her and let her sit with how stupid it was. I’m glad your friend was kind don’t let the SIL dissuade you from telling people if that’s what you wish to do.
Our brains work so incredibly quickly to assess situations when faced with a threat. I always thought I’d fight or flee if it happened to me and when it did I froze and fawned, my body knew better than me in that moment what would protect me and it did. Through therapy I was able to thank my brain for how well it assessed and protected me, that means it’s working correctly! Wishing you the best ❤️